UNIVERSITY  OF  CALIFORNIA 
AT  LOS  ANGELES 


GIFT  OF 

MRS. JOHN    C.SHEDB 


LABORATORY  EXERCISES 


TO  ACCOMPANY 


CARHART  AND   CHUTE'S 
FIRST  PRINCIPLES  OF  PHYSICS 


BY 
ROBERT  W.   FULLER 

AND 

RAYMOND    B.   BROWNLEE 

STUYVESANT   HIGH   SCHOOL,   NEW   YORK  CITY 


ALLYN    AND    BACON 

Boston  Itfeto  gork  C 


COPYRIGHT,    1912  AND  1913,   BY 

ROBERT  W.   FULLER 
AND  RAYMOND  B.  BROWNLEE 


F151 


PREFACE 

IN  the  preparation  of  a  Physics  laboratory  manual,  it  is  nec- 
essary to  take  into  account  the  diversity  of  courses  and  equip- 
ment in  different  schools.  The  individuality  of  the  teacher 
and  the  limitations  of  equipment  have  been  recognized  in  the 
selection  and  treatment  of  topics,  in  these  Exercises,  and  a  wide 
choice  of  experiments  has  been  provided,  only  a  few  of  which 
require  highly  specialized  apparatus.  Where  such  apparatus 
is  decidedly  superior  to  that  commonly  used,  specific  directions 
for  its  preparation  have  been  given  in  footnotes.  Experiments 
which  have  proved  their  value  in  generally  accepted  courses 
have  been  retained  with  such  simplifications  as  seem  desir- 
able to  secure  directness.  Other  experiments  which  repre- 
sent the  more  modern  trend  in  Physics  teaching  are  introduced 
in  considerable  number  to  enrich  the  course. 

Many  students  lose  the  value  of  the  laboratory  period  be- 
cause  it  is  spent  in  following  directions  in  a  purely  mechanical 
way,  while  they  wonder  why  the  particular  problem  on  which 
they  are  engaged  should  be  done  at  all.  In  order  to  settle 
this  question  in  the  student's  mind,  the  authors  have  been  in 
the  habit  of  furnishing  their  students  with  an  introductory 
paragraph  for  each  experiment.  This  introduction  connects 
the  experiment  with  the  pupil's  experience  and  furnishes  defi- 
nitions  of  such  terms  as  are  necessary  to  the  understanding  of 
the  directions.  This  introductory  paragraph  also  permits  the 
laboratory  experiment  on  a  particular  topic  to  be  given  either 
before  or  after  the  subject  is  discussed  in  class,  as  the  instructor 
may  desire. 

Following  the  plan  of  the  best  laboratory  manuals,  definite 
provision  has  been  made  for  recording  observations  and  calcu- 
lated results  either  in  tabulations  or  in  simple  diagrams.  This 
plan  permits  the  student's  record  to  be  made  in  a  minimum 
time  and  leaves  a  larger  proportion  of  the  period  available  for 
actual  laboratory  work  and  the  consideration  of  results  than  is 
possible  when  a  running  record  is  made.  It  also  reduces  the 


iv  PREFACE 

time  necessary  for  the  instructor  to  judge  the  accuracy  of  the 
student's  results,  as  well  as  his  grasp  of  the  principles  involved. 

The  Conclusion  always  calls  for  a  definite  answer  to  the 
question  which  is  raised  in  the  Object  of  the  experiment. 
Other  important  facts  or  principles  which  may  be  deduced  in 
connection  with  the  experimental  work  are  subjects  for  ques- 
tions in  the  Discussion.  These  may  be  answered  orally  as  the 
instructor  passes  from  student  to  student,  or,  in  large  classes 
particularly,  the  answers  may  be  written  in  the  note-book.  In 
any  case,  these  questions  direct  attention  to  the  salient  points 
of  the  experiment  and  should  be  taken  up  in  the  quiz  on  the 
laboratory  work. 

The  authors  wish  to  express  their  grateful  appreciation  of 
the  assistance  which  they  have  received  in  the  preparation  of 
this  book.  Among  their  associates  in  the  Stuyvesant  High 
School  they  are  particularly  indebted  to  the  principal,  Dr.  E. 
K.  von  Nardroff  for  valuable  suggestions  and  for  the  stimulus 
which  his  interest  in  the  experiments  has  afforded;  to  their 
colleagues  in  the  Physical  Science  Department,  particularly 
Mr.  J.  G.  Baier  and  Mr.  H.  W.  Mott,  for  many  helpful  criti- 
cisms and  suggestions;  and  to  Dr.  H.  E.  Fritz,  for  valuable 
assistance  in  the  preparation  of  the  drawings.  Many  of  the 
drawings  have  been  made  by  the  following  students :  Charles 
E.  O'Rourke  and  Harold  Jay,  of  the  Stuyvesant  High  School, 
and  John  G.  Smith,  of  the  Geneseo  Normal  School.  In  connec- 
tion with  particular  experiments,  acknowledgment  is  made  to 
the  teachers  who  rendered  assistance  in  these  experiments. 
Thanks  are  tendered  also  to  Professors  Carhart  and  Chute  for 
permission  to  use  several  cuts  (Figs.  3,  35,  68,  and  112)  from 
the  "  First  Principles  of  Physics  "  ;  to  Professor  W.  H.  Timbie 
for  the  use  of  the  Eesistance  Table  (p.  315)  from  his  "Ele- 
ments of  Electricity";  and  to  the  L.  E.  Knott  Apparatus 
Company  for  the  use  of  several  cuts. 

The  authors  will  gladly  receive  criticisms  and  suggestions 
from  teachers  who  may  use  the  Exercises  in  their  classes. 

R.  W.  F. 
R.  B.  B. 

FEBRUARY,  1913. 


CONTENTS 

PAGB 

Suggestions  to  the  Instructor 1 

Directions  to  Students 9 

Mechanics 

KXPERIMEKT 

1.  Metric  Units  of  Measurement    .....  18 

2.  Properties  of  Materials      .         .         .         .         .         .21 

3.  Measurement  of  Bodies    ......  24 

4.  Volume  Measurement  of  an  Irregular  Body         .         .  30 

5.  Density .32 

6.  Elasticity— Hooke's  Law          .         .         .         .         .34 

7.  Tenacity  of  Wire 37 

8.  Relation  between  Pressure  and  Depth        ...  40 

9.  Archimedes'  Principle 43 

10.    Law  of  Flotation 45 

10.  (Alternative)   Law  of  Flotation          ....  46 

11.  Specific  Gravity  of  Solids 48 

12.  Specific  Gravity  of  a  Liquid  (Bottle  Method)      .         .  50 

13.  Specific  Gravity  of  a  Liquid  (Hydrometer  Method)      .  52 

14.  Specific  Gravity  of  a  Liquid  (Hare's  Method)      .         .  55 

14.  (Alternative)   Specific  Gravity  of    Liquids  (Balancing 

Columns)     ........  58 

15.  Density  of  Air 62 

15.  (Alternative)  Density  of  Air 65 

16.  Boyle's  Law 68 

17.  Measurement  of  Gas  Pressure  .  71 


yi  CONTENTS 

EXPERIMENT  PAO« 

18.  Water  Pumps 74 

19.  Principle  of  Moments 77 

20.  Lever  Arm  of  a  Force      .  '       .         .         .         .         .80 

2 1 .  Composition  of  Several  Parallel  Forces      .         .         .       82 

22.  Four  Forces  at  Right  Angles    ...         .         .         .85 

23.  Parallelogram  of  Forces   .         ..        ....         .87 

24.  Resolution  of  Forces         .....         .         ...       90 

25.  Force  at  the  Center  of  Gravity  of  a  Body  .         .         .       93 

26.  Pendulum         ........       96 

27.  Inclined  Plane •     .       99 

28.  Pulleys 102 

29.  Wheel  and  Axle 107 

30.  Mechanical  Efficiency  of  Machines    .         .         .         .110 

31.  Coefficient  of  Friction       .         .         .•        .         .         .113 

Sound 

32.  Vibrations  of  a  Tuning  Fork 116 

33.  Velocity  of  Sound  in  Air 120 

34.  Sympathetic  Vibrations 122 

35.  Wave  Length  of  a  Sound 125 

36.  Laws  of  Vibrating  Strings 129 

Light 

37.  Measurement    of    Candle    Power  —  Jolly   or    Bunsen 

Photometer 133 

37.  (Alternative)  Measurement  of  Candle  Power  —  Rum- 

ford  Photometer 136 

38.  Law  of  Reflection  of  Light        .         .         .         .         .-139 

39.  Images  in  a  Plane  Mirror 142 


CONTENTS  Vii 

EXPERIMENT  PAO* 

40.  Reflection  in  a  Concave  Mirror          .         .         .         .144 

41.  Reflection  in  a  Convex  Mirror  .         .         .         .         .148 

42.  Refraction  through  a  Glass  Plate        .         .         .  '      .     1 49 

43.  Refraction  through  a  Prism 151 

44.  Index  of  Refraction 153 

45.  Total  Reflection    '•*.'.         .         .         .         .         .     155 

46A.    Study  of  a  Converging  Lens    .         .         .         .         .159 

46  B.    Focal  Length  of  a  Converging  Lens         .         .         .164 

47.  Conjugate  Foci  of  a  Converging  Lens         .         .         .166 

48.  Magnifying  Power  of  a  Lens  '  •."•       .                  .         .169 
49A.    Astronomical  Telescope      ''.         .         .         .         .172 
49B.    Compound  Microscope 176 

50.  Dispersion  of  Light  by  a  Prism          .         .         .         .179 

Heat 

51.  Fixed  Points  of  a  Thermometer         .         .         .         .181 

52.  Phenomena  of  Boiling       .         .         .         .         .         .185 

53.  Coefficient  of  Linear  Expansion          .         .         .         .190 

54.  Coefficient  of  Cubical  Expansion        .         .         .         .193 

55.  Increase  in  Volume  of  a  Gas  at  Constant  Pressure      .     197 

56.  Increase  in  Pressure  of  a  Gas  at  Constant  Volume       .     201 

57.  Law  of  Heat  Exchange 205 

58.  Specific  Heat  of  a  Metal 209 

59.  Cooling  through  Change  of  State        .         .         .         .213 

60.  Melting  Points  and  Boiling  Points      .         .         .         .216 

61.  Heat  Changes  during  Solution  and  Evaporation  .         .     220 

62.  Heat  of  Fusion  of  Ice 223 

63.  Heat  of  Vaporization 226 

64.  Dew  Point  230 


viii  CONTENTS 

Magnetism  and  Electricity 

EXPERIMENT  PAGE 

65.  Magnetic  Induction 232 

66.  Magnetic  Lines  of  Force 235 

67.  Development  of  an  Electrostatic  Series      .         .         .  238 

68.  Simple  Cell 241 

69.  Two-fluid  Cell 244 

70.  Electroplating  .     ' 247 

71.  Electrotyping  .         .         .         .         .         .         .         .250 

72.  Storage  Cell 252 

73.  Laws  of  Resistance       • 255 

74.  Effect  of  Temperature  on  Resistance          .         .         .  258 

75.  Internal  Resistance  of  a  Cell      .         .  .         .  26 1 

76.  Grouping  of  Cells 263 

77.  Resistance  and  Current  in  a  Divided  Circuit       .         .  266 

78.  Resistance  by  Substitution 269 

79.  Heating  Effect  of  an  Electric  Current         .         .         .  272 

80.  Study  of  an  Incandescent  Lamp         ....  276 

8 1 .  Lines  of  Force  around  a  Conductor  ....  278 

82.  Electromagnet          .         .         .         .         .         .         .281 

83.  Electric  Bell  . 284 

84.  Telegraph  Instruments 286 

85.  Operation  of  an  Electric  Motor  ....  288 

86.  Power  and  Efficiency  of  a  Motor        ....  290 

87.  Relation  between  Fall  of  Potential  and  Resistance       .  296 

88.  Resistance  by  the  Wheatstone  Bridge         .         .         .  298 

89.  Induced  Currents ,  302 

90.  Study  of  a  Dynamo  . 304 


CONTENTS        .  ix 

Appendix 

PAGE 

I.  Important  Numbers  and  Equivalents       .         .         .     309 

II.     Properties  of  Materials 310 

III.  Density  of  Water 312 

IV.  Index  of  Refraction 312 

V.  Electromotive  Farce  of  Cells         .         .         .         .312 

VI.  Table  of  Natural  Sines  and  Tangents  .  .  .313 
VII.  Size  and  Resistance  of  Annealed  Copper  Wire  .  314 
VIII.  Specific  Resistance  and  Temperature  Coefficient  .  315 


INTRODUCTORY 

SUGGESTIONS    TO    THE  INSTRUCTOR 

Selection  of  Experiments 

Scope  of  the  Experiments.  —  The  experiments  in  this  book 
provide  a  wide  range  of  laboratory  work  for  an  elementary 
course  in  Physics.  The  exercises  have  been  selected  on  the 
basis  of  their  educational  value  to  the  student.  Their  aim  is 
to  impart  to  him  certain  fundamental  principles,  to  acquaint 
him  with  some  physical  phenomena  qualitative  in  character, 
and  to  show  the  operation  and  the  use  of  practical  devices  or 
instruments  that  are  applications  of  physical  principles. 

The  authors  have  not  hesitated  to  omit  from  their  list 
certain  well-known  experiments  which  have  persisted  in  many 
elementary  courses,  rather  by  inertia  than  because  of  any 
special  interest  or  value  to  the  beginner.  On  the  other  hand, 
it  is  impossible  to  include  in  a  small  book  all  the  experiments 
of  merit  suitable  to  a  first  course  in  Physics.  Yet,  from 
those  given,  it  will  be  possible  for  any  instructor  to  make  a 
selection  of  the  experiments  which  the  great  majority  of 
Physics  teachers  include  in  their  courses,  so  as  to  afford  a 
well-balanced  laboratory  training,  both  interesting  and  instruc- 
tive to  the  student. 

Recommended  Lists.  —  Only  the  institutions  most  favored  as 
to  laboratory  time  will  be  able  to  complete  in  one  scholastic 
year  all  the  experiments  outlined  in  this  book.  Any  choice 
of  experiments  must  depend  upon  the  apparatus  available  and 
upon  the  laboratory  conditions.  To  fit  the  usual  laboratory 
equipment  and  to  meet  the  time  limitations  of  most  first 
courses  in  the  subject,  the  authors  suggest  the  following  list 
of  thirty-five  experiments  as  affording  a  good  training  in  those 
1 


2  GENERAL  SUGGESTIONS 

fundamentals  of  the  science  most  suitable  for  laboratory  in 
struction : 

FUNDAMENTAL  COURSE 

Mechanics:    Exercises  3,  4,  5,  8,  9,  10,  11,  19,  23,  25,  26,  27. 
Sound :     Exercise  35. 

Light:    Exercises  37,  38,  39,  42,  43,  46  A,  or  46 B  and  47. 
fiectf :    Exercises  51,  58,  59,  61,  62. 

Magnetism  and  Electricity :     Exercises  66,  68,  69,  70,  80,  81,  82, 
83,  84,  85,  89. 

The  following  ten  exercises  will  supplement  the  above, 
particularly  for  those  students  whose  ability  enables  them 
to  do  a  maximum  amount  of  work : 

Mechanics,  6,  13  or  14,  28,  29 ;       Heat,  57 ; 
Sound,  34 ;  Magnetism  and  Electricity,  72, 

Light,  44;  78  (or  other  experiment 

on  resistance),  90. 

The  following  sixty  exercises  are  suggested  as  a  more 
extended  course  for  those  institutions  favored  with  about 
double  the  laboratory  time  usually  allotted  to  the  first  course : 

EXTENDED  COURSE 

Mechanics:  Exercises  1,  3,  4,  5,  8,  9,  10,  11,  15,  16,  17,  19, 
20,  23,  24,  25,  26,  27,  28,  29,  30. 

Sound :  Exercises  32,  34,  35. 

Light :   Exercises  37, 38, 39, 42, 43, 44, 46  A,  or  46  B  and  47, 48. 

Heat:  Exercises  51,  52,  57,  58,  59,  60,  61,  62,  63. 

Magnetism  and  Electricity:  Exercises  65,  66,  68,  69,  70,  72, 
73,  78,  79,  80,  81,  82,  83,  84,  85,  86,  89,  90. 

/The  authors  recommend  the  following  list  of  experiments 
/tor  girls,  especially  for  those  not  intending  to  go  beyond  the 
/  high  school.     Most  of  these  experiments  have  been  selected  be- 
/    cause  of  their  close  relationship  to  the  practical  affairs  of  life. 

Mechanics:  Exercises  1,  2,  3,  6,  8,  9,  12  (or  13  or  14),  17, 18, 
\    23,26,27,28. 

VI 


TO  THE  INSTRUCTOR  3 

Sound:   Exercises  34  (or  35),  36. 
Light :   Exercises  37,  38,  39,  49,  50. 
Heat:  Exercises  51,  52,  59,  60,  61,  64. 

Magnetism  and  Electricity :  Exercises  65,  68,  70,  79,  80,  82, 
83,  84. 

A  number  of  interesting  and  valuable  experiments  do  not 
appear  in  any  of  the  preceding  lists,  but  it  is  hoped  that  some 
of  them  will  be  taken  from  time  to  time  either  as  substituted 
or  as  additional  exercises.  A  limited  amount  of  variation 
from  year  to  year  adds  interest  and  vitality  to  any  laboratory 
course.  Many  of  the  experiments  just  referred  to  will  meet 
the  needs  of  those  instructors  who  desire  to  give  more  time"  to 
certain  divisions  of  the  subject. 

Order  of  Experiments. — The  order  in  which  the  divisions  of 
the  subject  are  taken  should  depend  upon  the  aim  of  the 
course  and  the  conditions  under  which  it  is  given.  In  their 
own  work  the  authors  find  the  most  satisfactory  order  to  be 
Mechanics,  Heat,  Sound,  Electricity,  and  Light.  In  most 
syllabi,  however,  the  subj  ect  of  Light  precedes  that  of  Electricity. 
In  the  view  of  many,  the  experiments  on  Heat  are  best  adapted 
to  the  student's  powers  after  he  has  finished  the  experiments 
in  Mechanics. 

>Time  required  for  Experiments. — A  majority  of  the  experi- 
ments are  designed  to  take  from  80  to  90  minutes  of  laboratory 
time,  including  the  writing  of  the  note-book  record.  Some  of 
the  shorter  ones  will  require  but  half  of  that  time,  or  a  single 
school  period.  Even  if  a  double  laboratory  period  is  not 
available  for  the  longer  experiments,  the  directions  have  been 
written  so  that  the  experiments  can  be  done  successfully  in 
two  single  periods.  The  system  recommended  for  the  note- 
book record  saves  time  in  securing  the  observational  data. 
Especial  care  has  been  taken  not  to  overload  the  student  with 
more  manipulations  and  observations  than  would  be  reason- 
able for  an  average  rate  of  work  within  the  time  allotment. 


4  GENERAL  SUGGESTIONS 

The  Experimental  Directions 

Aim.  —  At  first  sight  it  may  seem  that  the  directions  for  the 
experiments  have  been  written  in  a  rigid  form  which  may 
hamper  the  individuality  of  the  teacher  using  them.  With 
the  possible  exception  of  the  placing  of  the  tables  of  observa- 
tions and  calculated  results,  it  will  be  found  that  the  directions 
and  their  requirements  are  in  accord  with  the  usages  which 
have  become  generally  established  as  leading  to  intelligent  and 
efficient  laboratory  work. 

The  five  main  divisions  of  the  printed  directions  are 
"Introductory,"  "Experimental,"  "Calculated  Kesults,"  "Dis- 
cussion," and  "Conclusion."  Certain  suggestions  as  to  these 
divisions  appear  in  the  paragraphs  that  follow. 

Introductory.  —  The  paragraphs  under  this  heading  in  the 
printed  directions  serve  several  purposes.  First,  they  awaken 
the  student's  interest  in  the  problem  to  be  studied  by  reference 
to  applications  of  Physics  more  or  less  familiar  to  him.  Sec- 
ondly, the  introductory  statements  show  the  relation  between  the 
practical  applications  and  the  laboratory  problem  to  be  solved. 
In  some  cases  the  paragraphs  furnish  a  little  theoretical  in- 
formation, necessary  for  the  intelligent  performance  of  the 
experiment.  All  that  is  required  of  the  student  is  that  he  read 
and  understand  this  introductory  matter  —  usually  a  task  of  a 
few  minutes.  It  is  not  expected  nor  is  it  desired  that  the  in- 
troductory matter  be  copied  into  the  note-book. 

The  authors  offer  no  apology  for  the  paragraphs  introduc- 
tory to  the  experiments.  They  have  simply  put  in  written 
form  those  preliminary  remarks  that  many  instructors  find 
desirable  to  make  when  the  class  assembles  for  the  experiment. 
It  is  felt  that  the  written  form  has  the  advantage  of  being  al- 
ways available  for  the  student's  reference. 

Experimental.  —  Whenever  the  length  and  character  of  the 
experiment  permits,  the  laboratory  problem  is  presented  as  a 
whole  to  the  student.  With  the  general  plan  in  mind, '  he  is 
able  to  do  the  experiment  with  greater  self-reliance  and  effi- 


TO   THE  INSTRUCTOR  5 

ciency  than  can  be  obtained  from  the  slavish  following  of 
detailed  directions  with  little  grasp  of  their  intent. 

In  some  experiments,  however,  detailed  directions  must  be 
given  to  secure  the  successful  imparting  of  a  series  of  experi- 
mental facts.  In  such  cases  the  divisions  are  made  as  few  as 
possible  and  their  meaning  made  clear  by  brief  directions,  a 
little  supplementary  information,  and  questions  that  the  aver- 
age student  should  be  able  to  answer  from  his  experimental 
observations. 

The  students  are  directed  to  place  the  data  gathered  in  the 
experiment  in  a  table  of  observations  near  the  top  of  the  left- 
hand  page  of  the  note-book  record.  The  form  for  this  table  is 
usually  furnished,  and  it  is  strongly  recommended  that  the 
student  write  the  form  in  the  note-book  before  making  any  of 
the  measurements.  This  procedure  provides  for  the  orderly 
recording  of  the  data  as  soon  as  it  is  obtained,  and  insures  the 
completion  of  the  experimentation  within  the  laboratory  hour. 
There  is  economy  also  of  the  instructor's  time,  as  he  can 
quickly  note  the  rate  of  progress  of  the  individual  and  check 
inaccuracies  in  the  readings. 

With  most  experiments  only  one  set  of  readings  is  indicated 
in  the  tables  of  observations,  but  the  instructor  desiring  more 
can  increase  the  number  of  columns  at  the  right.  In  the 
opinion  of  the  authors,  much  time  is  wasted  by  requiring  the 
duplication  of  readings  by  the  elementary  student  of  Physics, 
unless  in  work  where  personal  errors  are  large. 

Drawings.  —  After  the  observations  are  completed,  the 
student  is  directed  to  make  sectional  or  outline  drawings  from 
his  apparatus  so  as  to  show  that  he  understands  its  arrange- 
ment and  operation.  Many  of  the  illustrations  in  this  book 
have  been  made  from  drawings  made  by  students  in  the  regular 
course  of  their  laboratory  work.  Such  drawings  will  indicate 
to  the  users  of  this  book  the  methods  of  representing  labora- 
tory apparatus  by  simple  outline  drawings.  The  development 
of  a  simple  scheme  of  sectional  representation  is  within  the 
power  of  any  student  and  will  prove  most  useful  to  him. 


6  GENERAL  SUGGESTIONS 

Descriptions.  —  The  table  of  observations  and  the  sectional 
drawings  render  unnecessary  long  and  elaborate  descriptions  of 
the  experimental  work.  All  that  is  asked  is  a  brief  but  clear 
statement  of  the  general  method  of  the  experiment  and  the 
recording  of  any  experimental  facts  not  shown  by  the  draw- 
ings nor  provided  for  in  the  table  of  observations.  In  the 
last  few  years  it  has  become  more  and  more  recognized  that 
the  chief  function  of  the  laboratory  note-book  is  to  show  the 
essentials  of  an  experiment  and  not  to  provide  useless  drudgery 
for  the  student. 

Calculated  Results. —  Preceding  the  table  of  calculated  results 
occurring  in  many  experiments,  are  found  directions  for  mak- 
ing the  calculations.  The  authors  have  not  hesitated  to  fur- 
nish information  to  aid  the  student  in  making  the  calculations 
when  these  are  rendered  more  intelligible  thereby. 

The  directions  call  for  the  placing  of  the  table  of  calculated 
results  at  the  top  of  the  right-hand  page  of  the  note-book  record. 
The  calculations  themselves  should  be  made  directly  below  the 
table.  These  requirements  secure  prominent  and  convenient 
locations  for  the  making  of  the  computations  and  the  orderly 
recording  of  the  results.  The  student  can  tell  from  the  tabular 
form  what  is  expected  of  him  in  the  way  of  calculations  and 
knows  when  his  work  is  finished.  The  instructor  is  enabled 
to  check  quickly  the  recorded  results  and  to  point  out  during 
the  laboratory  period  sources  of  error. 

Discussions.  —  Under  this  division  the  student  is  directed  to 
answer  any  italicized  questions  occurring  in  the  experimental 
directions  or  the  questions  under  the  printed  heading,  Piscus- 
sion.  Thus  the  theoretical  considerations  of  the  experiment 
are  brought  together  ready  for  reference  or  correction. 

Conclusions.  —  The  student  is  either  required  to  state  for 
himself  the  formal  conclusion  justified  by  the  experimental 
facts,  or  to  complete  a  partial  statement  by  filling  in  the  in- 
dicated blanks.  The  latter  method  is  preferred  in  those  cases 
where  a  complete  and  well-worded  conclusion  is  difficult  for 


TO  THE  INSTRUCTOR  7 

the  student  to  formulate.  The  vital  part  of  the  statement 
must  be  furnished  by  the  student  and  requires  thought  on  his 
part. 

Method  of  Laboratory  Work.  —  Many  of  the  advantages  of 
having  the  note-book  record  follow  a  definite  plan  have  been 
discussed  under  the  topics  preceding  this.  Tabular  forms  for 
the  observations  and  the  calculated  results  are  appreciated  by 
many  instructors  as  leading  to  that  economy  of  laboratory 
time  which  gives  the  best  opportunity  for  experimentation  and 
reflection.  The  forms  for  such  tabulations  may  be  written  in 
the  note-book  prior  to  the  laboratory  hour  and  the  general  plan 
of  the  experiment  studied. 

The  authors  believe  that  it  is  not  only  permissible,  but  highly 
desirable,  for  the  student  to  know  before  he  comes  into  the 
laboratory  what  he  is  to  do.  They  require  their  own  students 
to  carefully  study  the  experiment  and  to  write  the  blank  table 
of  observations  in  the  note-book  before  coming  to  the  laboratory. 
Except  in  the  case  of  very  complicated  experiments,  the  student 
is  not  allowed  to  have  the  experimental  directions  before  him 
until  he  has  taken  all  readings  and  completed  his  drawing  and 
description.  He  is  then  allowed  to  refer  to  his  direction  sheet 
for  guidance  as  to  his  calculations  and  conclusions.  It  has 
been  found  that  under  this  plan  the  work  in  the  laboratory  is 
more  intelligent  and  less  of  the  "  cook-book  "  order.  Further- 
more, schools  having  only  single  laboratory  periods  may  be 
certain  of  having  the  readings  taken  and  the  experiment 
described  during  the  laboratory  period,  while  calculated  results 
and  conclusions  may  be  worked  out  the  next  day  either  in 
laboratory  or  classroom,  or,  if  desired,  done  as  part  of  the  home 
lesson  for  the  day  following  that  of  the  laboratory  period. 

No  factor  contributes  more  to  the  success  of  a  laboratory 
course  than  having  the  apparatus  tested  and  entirely  ready  for 
the  student  when  he  enters  the  laboratory.  Then  only  is  it 
possible  for  him  to  put  the  apparatus  together  and  start  its 
operation  without  loss  of  time,  so  that  the  readings  can  be 
made  comfortably  within  the  period. 


8  GENERAL  SUGGESTIONS 

Note-book  Directions.  —  On  page  16  there  will  be  found 
brief  instructions  intended  for  the  student  and  relating  to  the 
form  of  the  note-book  record.  Any  orderly  plan  must  have 
definiteness;  so  it  becomes  necessary  to  designate  left-hand 
and  right-hand  pages  for  certain  purposes.  These  directions 
may  reverse  the  usage  of  some  instructors,  but  it  is  hoped 
that  they  will  realize  it  makes  little  difference  whether  the 
left-hand  page  or  the  right-hand  page  serves  a  certain  purpose, 
so  long  as  there  is  a  definite  systematic  plan  to  make  the  note- 
book record  a  help  to  the  student,  and  to  make  the  ever  present 
and  laborious  task  of  note-boot  correction  easier  for  the 
instructor. 


DIRECTIONS   TO   STUDENTS 

Balances 

Construction  of  Platform  Balances.  —  The  platform  balance  01 
trip  scale  is  a  simple,  equal  arm  lever  in  which  the  vertical 
displacement  of  either  arm  is  indicated  by  a  pointer  swinging 
across  a  horizontal  scale.  When  the  pointer  swings  approxi- 
mately equal  distances  on  each  side  of  the  center  division  on 
the  horizontal  scale,  the  two  lever  arms  are  balanced  and  the 
scale  is  said  to  be  in  equilibrium. 


Fig.  1.     Platform  Balance. 

The  construction  of  the  trip  scale  is  shown  in  Figs.  1  and  2 
on  this  and  the  following  page.  This  convenient  instrument 
for  weighing  is  too  often  misused  in  the  physical  laboratory 
and  poor  results  obtained  with  it.  With  the  observance,  how- 
ever, of  a  few  simple  precautions,  rapid,  accurate  weighings 
can  be  made  with  this  piece  of  apparatus. 

Adjustment  of  Platform  Balances.  —  Before  weighing  always 
see  that  both  platforms  are  clean  Then  touch  lightly  one 


10 


GENERAL  SUGGESTIONS 


Fig.  2.     Sectional  View  of  Balance. 


platform  and  note  whether  or  not  the  pointer  swings  freely 
and  equally  on  each  side  of  the  center  line  of  the  scale.  The 
pointer  should  oscillate  at  least  two  divisions  to  the  right  and 
to  the  left.  In  too  short  swings  the  friction  in  the  bearings 

makes  the  scale  rela- 
tively less  sensitive. 
Therefore  the  point- 
er's coming  to  rest  at 
the  center  point  is  no 
sure  indication  that 
the  two  arms  of  the 
scale  are  balanced  or 
in  equilibrium. 

In  case  the  pointer 
swings  to  a  distinctly 
greater  distance  on 
one  side  of  center, 

turn  the  thumb  nut  which  is  just  below  the  center,  so  that  the 
nut  moves  a  little  distance  towards  the  side  of  the  lesser  swing. 
Again  note  the  swings.  When  they  are  approximately  equal 
on  both  sides  of  center,  the  scale  is  adjusted  for  weighing. 

Handling  of  Weights. — Place  the  object  to  be  weighed  on 
the  left-hand  platform  or  pan  and  the  weights  on  the  right-hand 
platform.  In  adding  or  removing  weights,  prevent  with  the 
left  hand  the  movement  of  the  pans  until  the  change  of 
weights  has  been  made.  In  this  way  avoid  jarring  the  balance 
and  injuring  the  knife-edges. 

For  the  first  weight  select  the  one  which  in  your  opinion  is 
about  equal  to  the  object  being  weighed.  If  this  weight  is  too 
small,  take  it  off  and  replace  it  with  the  next  larger  one. 
Continue  in  this  way  until  you  have  the  largest  weight  which 
is  lighter  than  the  object.  Then  add  the  next  smaller  weight. 
Time-saving  weighing  means  the  systematic  use  of  the  next 
smaller  or  the  next  larger  weight,  as  the  case  may  be,  until 
the  scale  is  balanced. 

In  practice  the  graduated  beam  with  its  rider  enables  one  to 


TO  STUDENTS  11 

dispense  with  the  smaller  weights.  If  the  beam  is  graduated 
for  5  grains,  the  1-gram  and  the  2-grain  weights  are  not  used  ; 
with  a  10-gram  beam,  the  weights  below  10  grams  are  not 
necessary.  By  means  of  the  graduated  beam,  these  smaller 
weights  are  found  by  moving  the  rider  to  the  right  until  the 
balance  is  in  equilibrium.  Note  carefully  on  which  side  of 
the  rider  the  reading  should  be  made,  and  remember  that 
the  reading  can  be  made  to  tenths  of  a  gram. 

When  the  correct  weight  is  obtained,  count  carefully  the 
weights  on  the  right-hand  pan  and  add  the  weight  indicated 
on  the  beam.  Record  this  total  weight  at  once  in  the  labora- 
tory note-book. 

Return  the  weights  to  their  block,  or  case,  counting  as  you 
do  so.  Add  the  weight  indicated  on  the  beam  and  check  the 
weight  recorded  in  the  note-book.  Remove  the  object  from  its 
scale  pan.  A  scale  left  with  the  arms  unequally  balanced  soon 
loses  its  sensitiveness,  owing  to  unnecessary  wear  on  the 
bearings. 

Beam  Balances.  —  Another  form  of  balance  much  used  in  the 
physical  laboratory  is  the  beam  balance.  The  beam  in  this 
case  rests  at  its  center  point  on  a  knife-edge,  or  a  wedge,  sup- 
ported on  a  vertical  stand.  Pans  are  suspended  on  the  ends 
of  the  beam  either  by  hooks,  or  in  the  more  expensive  kinds  by 
stirrups  which  rest  on  knife-edges.  A  vertical  pointer  indi- 
cates on  a  small  graduated  scale  the  oscillations  of  the  beam. 
Some  beam  balances  have  on  one  arm  of  the  beam  a  rider, 
which  slides  along  a  graduated  scale  and  thus  indicates  the 
smaller  weights.  To  avoid  dulling  the  knife-edges,  there  is 
often  a  device  which  lifts  the  beam  off  the  knife-edges  when 
the  balance  is  not  in  use.  The  pan  arrest  similarly  lifts  the 
bow  and  stirrup  suspension  from  off  the  knife-edges  on  the 
ends  of  the  beam. 

The  specific  gravity  balance  is  usually  a  beam  balance  which 
has  a  shorter  suspension  for  one  of  the  pans.  From  a  hook  on 
the  under  side  of  this  pan  are  suspended  objects  which  are  to 
be  weighed  in  a  liquid. 


12  GENERAL  SUGGESTIONS 

The  hornpan  balance  is  simply  a  beam  balance,  which  is  sup- 
ported vertically  from  a  hook  hung  on  a  ring  stand  or  held  by 
the  hand. 

Spring  Balances.  —  A  spring  balance  measures  the  mass  of  a 
body  by  the  elongation  of  a  spiral  spring.  The  weight  is  in- 
dicated on  a  graduated  scale  by  a  pointer  attached  to  a  draw- 
bar on  the  free  end  of  the  spring.  Attached  to  the  drawbar 
is  a  hook  on  which  is  suspended  the  object  to  be  weighed. 

The  spring  balance  is  made  to  read  correctly  in  vertical 
position,  with  the  hook  downward.  The  weight  of  the  draw- 
bar and  hook  should  be  sufficient  to  bring  the  pointer  to 
the  zero  mark  on  the  graduated  scale.  If  the  pointer  does 
not  stand  at  zero  with  no  load  on  the  balance,  a  correction 
must  be  made  to  the  weight  registered  on  the  scale  in  order  to 
get  the  true  weight  of  the  object.  The  inconvenience  of  mak- 
ing these  corrections  may  sometimes  be  avoided  by  wrapping 
about  the  shank  of  the  hook  a  strip  of  sheet  lead,  sufficient  in 
weight  to  bring  the  pointer  to  the  zero  point  of  the  scale. 

The  friction  in  a  spring  balance  tends  to  make  less  accurate 
the  readings  in  the  first  portion  of  the  graduated  scale.  At  the 
other  end  of  the  scale,  when  the  spring  is  near  its  maximum 
stretch,  the  elongations  are  not  quite  proportional  to  the 
heavier  weights  added.  Accordingly  the  most  acciirate  read- 
ings with  a  spring  balance  are  those  obtained  in  about  the 
middle  portion  of  the  graduated  scale. 

In  some  experiments  the  spring  balance  is  used  to  measure 
the  pull  or  force  exerted  upon  its  spring.  When  used  for  this 
purpose  it  is  termed  a  dynamometer. 

Sensitiveness  of  a  Balance.  —  The  sensitiveness  of  a  balance 
may  be  defined  as  the  smallest  difference  which  is  indicated 
by  the  balance  with  a  given  load.  The  trip  scale  should  be 
sensitive  to  at  least  the  tenth  of  a  gram  with  an  ordinary  load, 
i.e.  show  a  difference  between  50.6  and  50.7  grams.  A  good 
hornpan  balance  indicates  weights  within  the  hundredth  of  a 
gram  (1  centigram)  while  an  accurate  chemical  balance  is  sen- 
sitive to  a  ten-thousandth  of  a  gram  (tenth  of  a  milligram). 


TO  STUDENTS  13 

Relative  Advantages  of  Platform  and  Beam  Balances.  —  The 
platform  balance,  while  it  is  easy  to  keep  clean  and  can  stand 
much  usage,  is  usually  not  so  sensitive  as  the  beam  balance. 
The  broad  platforms,  however,  are  very  convenient  for  weigh- 
ing bulky,  unstable  objects,  and  the  oscillations  of  its  beam 
are  easily  controlled. 

The  sensitiveness  of  a  beam  balance  is  gained  at  the  expense 
of  stability  and  durability,  for  the  beam  is  easily  displaced  and 
the  knife-edge  suspension  becomes  dulled  by  use.  On  this  ac- 
count great  care  should  be  taken  not  to  jar  the  balance  nor 
allow  the  beam  to  oscillate  too  rapidly.  The  weights  should 
be  placed  gently  upon  the  pans  and  removed  when  the  pans 
are  at  rest  (i.e.  supported  by  the  pan  arrest  or  by  the  hand). 

Were  it  not  for  the  awkwardness  and  carelessness  of  some 
students,  the  beam  balance  would  always  be  most  desirable  for 
rapid,  accurate  weighings  in  the  physical  laboratory. 


Electrical  Measuring  Instruments 

The  instruments  used  for  measuring  the  strength  or  the 
pressure  of  an  electric  current  have  very  delicate  parts  and 
may  be  easily  ruined  by  either  rough  usage  or  excessive 
current. 

Before  using  any  galvanometer  or  other  meter  the  student 
should  assure  himself  that  it  has  the  proper  scale  range  and 
current-carrying  capacity  for  the  work  in  hand.  He  must 
further  so  connect  his  apparatus  that  the  instrument  will  not 
be  upset  or  pulled  out  of  place  by  any  change  in  connections 
made  during  the  experiment.  As  the  several  instruments  that 
the  student  may  be  called  to  use  in  his  experiments  differ  in 
their  sensitiveness,  method  of  connection,  and  method  of  read- 
ing, each  kind  will  be  briefly  discussed  by  itself.  In  reading 
all  instruments,  tenths  of  the  smallest  divisions  should  be  esti- 
mated. 

Tangent  Galvanometer.  —  This  consists  of  a  compass  needle 
mounted  at  the  center  of  a  hoop,  on  which  is  wound  the  wire 


14  GENERAL  SUGGESTIONS 

which  is  to  convey  the  current.  This  is  the  most  rugged  ol 
the  instruments,  but  the  pivot  is  likely  to  be  bent  by  dropping 
or  violently  jarring  the  instrument.  Where  there  are  a  num- 
ber of  binding  posts,  to  permit  the  use  of  different  numbers  of 
turns  of  wire,  find  out  from  the  instructor  which  posts  to  use 
and  the  number  of  turns  of  wire  included  between  them.  In 
order  to  read  the  instrument  accurately,  it  should  be  so  placed 
on  the  table  that  it  will  be  possible  to  look  directly  down  on 
the  needle.  The  instrument  should  be  carefully  turned  until 
the  needle  is  in  the  plane  of  the  coil. 

D'Arsonval  Galvanometer.  —  The  moving  part  of  this  instru- 
ment is  a  light  coil  of  wire,  suspended  between  the  poles  of  a 
permanent  luagnet  by  a  fine  wire  or  ribbon  through  which  the 
current  passes.  This  suspension  is  exceedingly  thin,  so  that 
even  a  slight  shock  to  the  instrument  will  break  it  and  a 
comparatively  small  current  will  melt  it.  The  instrument  is 
commonly  provided  with  a  clamping  device  which  takes  the 
weight  of  the  coil  off  the  suspension  when  the  galvanometer  is 
not  in  use. 

In  setting  up  the  galvanometer,  keep  the  coil  clamped  until 
you  are  ready  to  connect  to  the  source  of  current.  Then  make 
sure  that  the  instrument  is  leveled  in  such  a  way  that  the  coil 
does  not  rub  against  any  part  of  the  instrument  but  hangs  per- 
fectly free.  The  method  of  reading  the  deflections  for  the 
particular  instrument  you  are  using  will  be  explained  by  the 
instructor. 

It  is  exceedingly  important  that  only  a  very  small  current 
pass  through  the  coil  of  the  instrument.  On  this  account,  the 
galvanometer  should  have  either  a  coil  of  high  resistance  in 
series  with  it  or  a  low  resistance  shunt  across  the  terminals  for 
most  experiments.  Such  additions  to  the  instrument  should 
be  made  either  by  the  instructor  previous  to  the  laboratory 
hour  or  under  his  immediate  direction  by  the  student. 

Ammeter. — The  commercial  form  of  this  instruin-ent  is 
usually  a  d'Arsonval  galvanometer  provided  with  a  shunt  of 


TO  STUDENTS  15 

such  resistance  that  the  deflections  of  the  needle  give  the  num- 
ber of  amperes  directly.  The  coil  is  pivoted  instead  of  being 
suspended,  but  the  instrument  must  be  guarded  against  falls 
and  shocks  just  as  a  fine  watch  would  be. 

Before  connecting  the  ammeter  in  circuit,  be  sure  that  its 
range  is  sufficient  for  the  current  to  be  measured.  If  the  in- 
strument has  more  than  one  range,  always  connect  for  the  largest 
range  first,  and  then  change  the  connections  to  those  for  a 
smaller  range,  if  the  readings  indicate  that  this  can  be  safely 
done. 

If  the  ammeter  has  an  external  shunt,  be  sure  that  the  con- 
nections between  the  shunt  and  the  instrument  movement  are 
tight.  A  loose  contact  will  certainly  make  an  incorrect  read- 
ing and  may  burn  out  the  instrument. 

Connect  the  terminals  of  the  instrument  .in  series  with  the 
circuit.  If  connected  in  shunt  with  the  other  apparatus,  the 
resistance  of  the  instrument  is  so  small  that  the  movement  will 
probably  be  burned  out. 

In  every  electrical  circuit,  there  should  be  a  switch  that  can  be 
opened  instantly  if  there  is  the  slightest  indication  of  too  much 
current  for  the  instruments  or  any  other  part  of  the  apparatus. 

Voltmeter. — This  is  similar  to  the  ammeter  in  construction, 
but  has  a  high  resistance  in  series  with  the  movement  instead 
of  a  shunt  across  the  movement.  The  voltmeter  measures 
pressure,  while  the  ammeter  measures  current  flow. 

The  same  precautions  for  handling  and  for  the  selection  of  a 
proper  scale  range  are  to  be  observed  as  in  the  case  of  the  am- 
meter. 

Connect  the  voltmeter  across  (in  shunt  with)  the  circuit  or 
that  part  of  the  circuit  in  which  the  voltage  drop  is  to  be 
measured. 

Resistance  Box.  —  The  voltage  applied  to  a  resistance  box 
should  never  be  great  enough  to  cause  more  than  0.1  ampere  to 
pass  through  the  box. 


16  GENERAL  SUGGESTIONS 

The  Laboratory  Note-book 

Unless  other  directions  are  given  by  the  instructor,  the  fol- 
lowing plan  should  be  followed  in  recording  experiments  in 
the  note-book. 

Number  of  Experiment.  —  Place  to  the  left  and  at  the  top  of 
the  left-hand  page. 

Date  of  Experiment.  —  Place  to  the  right  and  at  the  top  of 
the  left-hand  page. 

Title.  —  Place  immediately  below  the  number  and  date. 
Object.  —  Place  directly  below  the  title. 

Tables  of  Observations.  —  Place  immediately  below  the  object. 
In  case  the  instructor  desires  the  duplication  of  the  observa- 
tions, make  the  necessary  number  of  parallel  columns  at  the 
right.  Always  record  the  measurements,  as  soon  as  made,  in 
the  tabular  form.  Decimals  should  be  used,  rather  than  com- 
mon fractions. 

The  number,  the  date,  the  title,  the  object,  and  the  table  of 
observations  should  be  written  in  the  note-book  before  the 
experimental  work  is  begun. 

Drawings.  —  Place  on  the  left-hand  page  clear  sectional 
drawings  showing  the  arrangement  and  operation  of  your  ap- 
paratus. In  making  a  sectional  drawing,  imagine  a  vertical 
plane  passing  through  the  middle  of  your  apparatus ;  then 
imagine  your  paper  to  be  in  the  position  of  this  plane.  Draw 
lines  where  the  paper  would  touch  the  intersected  apparatus. 

Descriptions.  —  Place  these  usually  on  the  left-hand  page  and 
shorten  your  work  by  referring  to  your  drawings.  A  simple, 
clear  account  of  the  general  method  of  the  experiment  is  prefer- 
able to  an  elaborate  description. 

Table  of  Calculations.  —  Place  at  the  top  of  the  right-hand 
page  before  making  any  of  the  calculations.  Do  the  mathe- 


TO  STUDENTS  17 

matical  work  involved,  immediately  below  the  table,  and  record 
the  results  as  soon  as  obtained  in  the  tabular  form. 

Discussion.  —  Under  this  heading  on  the  right-hand  page, 
answer  any  italicized  questions  occurring  in  the  experimental 
directions  as  well  as  the  questions  under  the  printed  heading 
of  "  Discussion."  If  more  room  is  necessary,  continue  on  the 
next  right-hand  page. 

Conclusion.  —  Place  under  this  heading  on  the  right-hand 
page,  immediately  following  the  Discussion. 

Introductory. — It  will  pay  you  to  read  and  understand  this, 
before  beginning  the  experimental  work.  It  is  not  to  be  copied 
into  the  laboratory  note-book. 


LABORATORY   EXERCISES 

EXPERIMENT   1 

Metric  Units  of  Measurement 

OBJECT.  To  become  familiar  with  the  units  of  metric  measure- 
ments commonly  used  in  scientific  work. 

APPARATUS.  Meter  stick ;  scissors ;  small  graduate  (50  or 
100  c.c);  large  graduate  (500  or  1000  cc);  liquid  quart  meas- 
ure; small  wide-mouth  bottle;  tumbler;  platform  balance ;  metric 
weights;  1  Ib.  weight. 

MATERIAL.  "Oak  tag,"  or  some  other  kind  of  stiff  paper; 
mucilage,  or  paste. 

Introductory : 

The  Metric  System  is  the  official  system  of  units  of 
measurement  in  most  civilized  countries.  It  is  the  system 
used  in  scientific  work  in  the  United  States.  The  unit 

100  MILLIMETERS  =  10  CENTIMETERS  =  1  DECIMETER  =  3.937  INCHES. 


nli  ii  iiiiifn 


INCHES  AND  TENTHS 

Fig.  3. 

of  this  system  is  the  meter,  and  standard  bars  with  this 
distance  marked  on  them  are  preserved  for  reference  by 
various  governments. 

•   The  Metric  System  is  a  decimal  system  and  therein 

lies  its  great  convenience.     The  meter  is  subdivided  into 

18 


METRIC  UNITS  OF  MEASUREMENT  19 

ten  parts,  each  of  which  is  termed  a  decimeter ;  the  hun- 
dredth of  a  meter  is  a  centimeter;   the  thousandth  of  a 
meter,  a  millimeter.     From  these  fundamental  units,  the 
units  of  surface,  volume,  and  weight  are  derived. 
The  meter  measures  39.37  inches. 

Experimental : 

At  the  top  of  the  left-hand  page  of  the  laboratory  note- 
book put  the  number  and  title  of  the  experiment  and  the 
date.  Then  state  the  object  of  the  experiment.  Immedi- 
ately below  this,  put  the  following  tabular  form  for  the 
readings  : 

OBSERVATIONS 

Length  of  note-book  cover cm. 

Width  of  note-book  cover cm. 

Metric  equivalent  of  liquid  quart       ....  cm.3 

Capacity  of  small  bottle cm? 

Capacity  of  tumbler cm.s 

Weight  of  note-book  ...... g. 

Metric  equivalent  of  a  pound  ......  a. 

Units  of  Length.  —  (a)  Examine  a  meter  stick,  noting 
its  subdivisions.  In  your  laboratory  note-book,  just  below 
the  table  of  observations,  rule  horizontal  lines  of  the  fol- 
lowing lengths,  labeling  each  line  with  its  length  : 

1  decimeter,  1.1  decimeters,  1.5  decimeters,  5  centimeters, 
2.5  centimeters,  1.3  centimeters,  1  centimeter. 

(6)  Measure  in  centimeters  and  tenths  of  a  centimeter 
the  length  of  the  cover  of  your  laboratory  note-book. 
Similarly  measure  the  width.  Record  the  dimensions. 

Units  of  Volume  and  Capacity.  —  (<?)  On  a  separate 
piece  of  paper,  lay  off  a  diagram  like  Fig.  4. 


20 


LABORATORY  EXERCISES 


Cut  around  the  diagram  with  a  pair  of  scissors.     Bend 
over  the  little  flaps   and   fold   into  a  cube,    pasting  the 
f — ^  flaps  on  the  inside  so  as  to 

hold  the  cube  together. 

The  little  cube,  if  accu- 
rately made,  is  a  cubic  centi- 
meter, the  unit  of  volume. 
1000  cubic  centimeters  give 
the  liter,  the  unit  of  capac- 


Fig.  5.     Dissected  Liter  Block. 


Fig.  4. 

ity.  For  convenience,  the 
measuring  instruments  for 
liquids  are  usually  cylindri- 
cal vessels,  marked  off  in 
cubic  centimeters  and 
known  as  graduates. 

(6?)  Using  a  large  gradu- 
ate, determine  how  many  cubic  centimeters  of  water  are 
needed  to  fill  an  ordinary  quart  measure. 

(To  be  done  in  groups  of  four  students  unless  otherwise  directed 
by  the  instructor.) 

(j&)  Using  a  small  graduate,  find  the  capacity  in  cubic 
centimeters  of  the  small  bottle  furnished  you. 

Similarly  determine  the  capacity  of  an  ordinary  drink- 
ing tumbler. 

Units  of  Weight.  —  The  weight  of  a  cubic  centimeter 
of  water  at  its  maximum  density  (4°  C.)  is  taken  as  the 
unit  of  weight,  the  gram. 

1000  grams  make  a  kilogram,  a  weight  used  for  measur- 
ing large  quantities. 


PROPERTIES  OF  MATERIALS  21 

(/)  Using  a  platform  balance,  find  the  weight  in  grams 
of  your  laboratory  note-book.  Record. 

(#)  Determine  how  many  grams  are  needed  to  counter- 
balance an  ordinary  pound  weight.  Record. 

Tables  for  the  calculated  results  should  be  placed  at 
the  top  of  the  right-hand  page  of  the  note-book,  and  the 
calculations  worked  out  just  beneath  them. 

Express  the  number  of  cubic  centimeters  found  in  (d~) 
as  the  decimal  part  of  a  liter.  Using  this  number,  calcu- 
late the  equivalent  of  a  liter  in  quarts,  carrying  the  result 
to  two  decimal  places. 

Calculate  from  the  comparison  of  weights  found  in  (#), 
the  equivalent  of  a  kilogram  in  pounds  and  tenths  of  a 
pound. 

CALCULATED  RESULTS 

1  liter qts. 

1  kilogram Ibs. 

Discussion  : 

In  what  respects  was  the  convenience  of  the  Metric 
System  shown  in  your  measurements?  Place  the  answer 
to  this  question  on  the  right-hand  page  of  the  note-book, 
heading  it  "  Discussion."  (Under  this  heading  are  to  be 
written  the  answers  to  any  italicized  questions  occurring 
in  the  experimental  directions.) 


EXPERIMENT   2 

Properties  of  Materials 

OBJECT.    To  examine  a  few  common  substances  so  as  to  deter- 
mine their  properties. 

APPARATUS.     Triangular  file  ;  pocket-knife  ;  hammer ;  anvil,  or 
flatiron  (with  detachable  handle). 


22 


LABORATORY  EXERCISES 


MATERIAL.  Copper  wire  $18,  or  some  larger  size  ;  strips  of 
sheet  lead  about  3£"  X  |";  pieces  of  small  glass  tubing  ;  paraf- 
fin grubber  bands,  or  strips  of  sheet  rubber ;  steel  nails. 

Introductory: 

Every  substance  has  its  own  set  of  properties.  Certain 
of  these  are  the  well-marked  or  characteristic  properties 
by  which  we  recognize  the  substance.  These  characteristic 
properties  are  important  in  that  they  determine  the  prac- 
tical use  of  a  substance. 

Experimental:  • 

The  substances  to  be  examined  are  copper,  glass,  rubber, 
lead,  paraffin,  wood,  and  steel.  Take  them  in  any  order. 
Tabulate  on  the  left-hand  page  of  your  note-book  the 
results  of  your  examination,  in  a  table  like  that  given 
below. 


SUBSTANCE 

HARDNESS 

LUSTRE 

MALLEABILITY 

ELASTICITY 

Copper 

Glass 

Rubber 

Lead 

Paraffin 

Wood 

Steel 

PROPERTIES  OF  MATERIALS  23 

Hardness.  — •  Use  a  knife  blade  or  a  file  to  determine 
the  hardness.  Describe  this  in  comparative  terms,  as 
very  soft,  soft,  somewhat  hard,  hard,  and  very  hard. 

Lustre.  —  Note  two  kinds  of  lustre  or  "  shine."  Which 
substances  would  be  said  to  be  without  lustre  ? 

Malleability.  —  Use  a  hammer,  and  tap  the  substance 
on  an  anvil  or  other  block  of  iron  to  ascertain  whether  or 
not  the  substance  can  be  hammered  out  into  sheets  with- 
out breaking. 

Elasticity.  —  Try  to  change  the  shape  of  the  substance 
by  bending.  If  the  substance  bends  or  gives,  remove  the 
strain  to  find  out  whether  or  not  the  substance  will  return 
to  its  original  condition.  In  determining  the  elasticity, 
make  use  of  the  results  obtained  in  testing  for  malleability. 

Ductility.  —  A  ductile  substance  admits  of  being  drawn 
out  into  fine  wire.  This  property  is  not  easily  determined 
in  the  laboratory  by  students.  Which  of  the  substances 
are  ductile  ?  Wliy  do  you  think  so  ?  Do  not  tabulate  for 
ductility. 

Write  a  simple  description  of  how  you  determined  each 
of  the  properties  tabulated.  No  drawing  is  necessary  for 
this  experiment. 

Discussion: 

Under  this  heading  on  the  right-hand  page  of  note- 
book, answer  any  italicized  questions  occurring  in  the 
experimental  directions,  and  also  the  following  questions: 
Which  of  the  substances  are  good  conductors  of  heat? 
Of  electricity?  Name  any  other  general  properties. that 
have  not  been  mentioned  in  this  experiment  (Class 
Discussion). 


24  LABORATORY  EXERCISES 

EXPERIMENT    3 

Measurement  of  Bodies 

OBJECT.    To  find  in  metric  units  the  volume  of  a  block  of  wood. 
APPARATUS.     Wooden  block ;  metric  scale. 

Introductory :  « 

Iron  is  "  heavier"  or  more  dense  than  wood.  To  find 
out  how  many  times  as  dense,  measurements  must  be  made 
of  the  size  and  weight  of  a  piece  of  each.  It  is  more  con- 
venient in  physical  work  to  make  the  measurements  in  the 
metric  system,  because  it  is  a  decimal  system.  The  chief 
units  used  are  the  centimeter  and  the  gram. 

Experimental : 

On  the  left-hand  page  of  your  note-book  and  immedi- 
ately below  the  statement  of  the  object  of  the  experi- 
ment, put  a  tabular  form  like  the  following  for  the 
measurements  to  be  made:  1 

OBSERVATIONS 

Number  of  block 

Length  of  block cm. 

Width  of  block cm. 

Thickness  of  block cm. 

When  the  scale  is  placed  so  that  the  scale  divisions  touch 
the  block,  there  will  be  less  error  in  reading  measurements. 

lrfote  to  Instructor.  Many  teachers  find  it  desirable  to  have  the 
students  write  in  their  laboratory  note-books,  previous  to  coming  into  the 
laboratory,  the  number,  the  title,  and  the  object  of  the  experiment,  and 
any  tabular  form  of  measurements  to  be  made.  As  this  will  be  the  first 
experiment  in  many  courses,  the  directions  for  the  note-book  record  have 
been  made  very  definite. 


MEASUREMENT  OF  BODIES  25 

The  eye  must  be  directly  in  front  of  the  point  on,  the  scale 
and  the  point  located  in  the  block.  Why  is  it  desirable 
to  estimate  to  hundredths  of  a  division  on  a  scale  divided 
into  tenths? 

Using  the  scale  in  this 
way,  find  the  length, 
breadth,  and  thickness  of 
the  block  furnished  you. 
Do  not  make  measure- 
ments at  bruised  corners.  Fig.  6. 

From     your     apparatus 

make,  on  the  left-hand  page  of  the  note-book,  an  outline 
drawing  similar  to  that  given  (Fig.  6). 

On  the  same  page  write  a  brief  description  of  what  you 
did,  touching  on  the  points  regarding  measurements  which 
you  were  instructed  to  observe.  Complete  in  the  laboratory 
at  least  the  drawing  and  the  description.  The  left-hand 
page  of  the  note-book  should  be  finished  before  the  right- 
hand  j?age  is  begun. 

On  the  right-hand  page,  place  the  table  of  calculated 
results,  the  calculations  themselves,  the  answers  to  the 
questions  for  discussion,  and  the  formal  conclusion.  The 
tables  of  calculated  results  should  always  be  placed  at  the 
top  of  the  right-hand  page. 


CALCULATED  RESULT 

Volume  of  block  .     .     .     .     .     . 


In  making  the  calculations  for  the  above  results,  indicate 
the  units  of  measurement  for  each  result.  Do  not  carry 
out  the  calculated  volume  beyond  the  hundredths  of  a 
cubic  centimeter.  Read  the  discussion  on  "Significant 
Figures,"  pages  27-29. 


26  LABORATORY  EXERCISES 

Discussion : 

Under  this  heading  on  the  right-hand  page  answer  any 
italicized  questions  occurring  in  the  experimental  direc- 
tions. Why  would  it  be  desirable  to  make  several  meas- 
urements of  each  dimension  of  the  block  and  take  the 
average  for  the  calculation  ? 

Conclusion : 

The  volume  of  block  No.  ..    ._  is  ._    ..  cm.8. 


SIGNIFICANT    FIGURES 

Accuracy  in  Scientific  Calculations.  —  Calculations  in  scientific 
work  are  based  on  readings  obtained  by  some  method  of  meas- 
urement. The  calculations  cannot  be  more  accurate  than  the 
figures  with  which  they  are  made.  Yet  beginners  in  physics, 
in  their  zeal  to  be  accurate,  retain  figures  in  their  calculations 
far  beyond  the  point  justified  by  the  accuracy  of  the  measure- 
ments. The  results  are  not  so  accurate  as  they  would  be 
if  certain  figures  had  been  discarded  in  the  progress  of  the 
calculations.  The  following  paragraphs  aim  to  show  how 
scientific  accuracy  may  be  obtained  in  the  calculations  of 
experimental  physics. 

Average  Readings  or  Results.  —  The  dimensions  of  a  rectan- 
gular block  may  be  measured  with  a  metric  scale  graduated  in 
centimeters  and  millimeters.  By  estimating  the  tenths  of  a 
millimeter,  the  readings  may  be  expressed  to  the  hundredths 
of  a  centimeter. 

The  following  readings  might  be  obtained  for  the  length  of 
the  block  as  determined  along  two  of  its  edges : 


3)22.34  cm.  3)22.34  cm. 

7.44  cm.  7.446  cm. 

(Correct  scientific  average.)  (Incorrect  scientific  average.) 

The  second  decimal  place  in  these  readings  represents  the 
estimated  tenths  of  a  milli meter.  In  estimating  such  small 
quantities,  one  may  readily  misjudge  not  only  by  one  tenth  of 

27 


28  LABORATORY  EXERCISES 

a  millimeter,  but  even  to  the  extent  of  two  or  three  tenths. 
Hence  the  figures  expressing  tenths  of  a  millimeter  are  not 
accurate,  but  are  doubtful  figures.  They  are  indicated  here  in 
heavy-face  type. 

In  column  B  the  average  given  for  the  three  readings  is 
7.446.  In  this  numbef  the  second  4  is  a  doubtful  figure,  there- 
fore the  6  in  the  next  decimal  place  beyond  must  be  more  than 
doubtful.  This  figure  6  means  nothing  in  our  units  of  meas- 
urement. 

Some  authorities  may  claim  that  7.45  is  nearer  to  the  correct 
average  in  such  a  case.  Mathematically  this  is  so,  but  it  must 
be  remembered  that  one  cannot  judge  accurately  between  0.04 
cm.  and  0.05  cm.  on  a  scale  whose  smallest  division  is  0.1  cm. 
Hence  the  average  of  7.44  in  column  A  may  be  regarded  by 
the  painstaking  student  as  correct  and  reasonable,  particularly 
as  the  divisor  is  a  small  number. 

Retention  of  Significant  Figures.  —  Let  us  find  the  volume  of 
a  rectangular  block  with  the  following  dimensions:  length, 
7.44  cm. ;  width,  4.67  cm. ;  and  height,  2.82  cm.  To  find  the 
area  of  the  base  multiply  the  length  by  the  width,  indicating 
the  doubtful  figures  in  heavy-face  type. 

7.44 
4.67 
5208 

4464 
2976 


34.7448  cm.2 

In  the  first  partial  product,  5208,  all  the  figures  are  doubt- 
ful, as  they  were  obtained  by  multiplying  by  the  doubtful 
figure  7;  in  the  second  partial  product,  4464,  the  final  4  is 
doubtful  because  it  resulted  from  a  multiplication  in  which  a 
doubtful  figure  was  a  factor ;  and  for  the  same  reason  the  6  in 
the  third  partial  product,  2976,  is  doubtful. 

In  the  addition  of  the  partial  products,  figures  which  are  ob- 


SIGNIFICANT  FIGURES  29 

tained  by  adding  doubtful  figures,  are  doubtful  figures.  This 
makes  the  last  four  figures  doubtful  in  the  total  34.7448.  All 
the  doubtful  figures  but  the  first  should  be  discarded.  Then 
the  area  of  the  base  as  justified  by  the  accuracy  from  measure- 
ments is  34.7  square  centimeters. 

To  find  the  cubical  contents  multiply  the  area  of  the  base  by 
the  height : 

34.7 

2.82 


2776 
694 


97.854  cm.8 

Discarding  all  the  doubtful  figures  except  the  first,  97.8  cm.8  is 
the  correct  volume  of  the  rectangular  block. 

A  student  who  found  the  cubical  contents  without  discard 
ing  any  of  the  doubtful  figures  would  get  as  a  result  97.980336 
cm.3.  Not  only  would,  he  have  done  extra  work,  but  his  result 
would  not  be  scientifically  accurate. 

A  good  rule  in  making  calculations  is  to  retain  only  signifi- 
cant figures.  Significant  figures  include  the  first  doubtful 
figure  and  the  figures  preceding  it. 


30 


LABORATORY  EXERCISES 


EXPERIMENT   4 

Volume  Measurement  of  an  Irregular  Body 

OBJECT.    To  find  the  volume  of  a  body  of  irregular  shape. 

APPARATUS.  Solid  of  irregular  shape,  .as  a  lump  of  metai, 
brass  hook  weight  (50  or  100  g.),  or  large-sized  lead  sinker; 
cylindrical  graduate  (100  c.c.)  ;  strong  thread,  or  string. 

Introductory : 

The  volume  of  a  body  of  irregular  shape  cannot  be 
found  by  measuring  a  few  dimensions  and  then  making  a 
simple  calculation.  A  stone  dropped  into  a  glass  of  water 
raises  the  water  level.  As  the  stone  and  the  water  can- 
not occupy  the  same  place  at  the  same  time,  the  volume 
of  the  stone  may  be  found  from  the  increase  in  volume. 

Experimental : 

Given  a  lump  of  metal  and  a  graduated  cylinder  with 
water  in  it,  devise  a  way  of  getting  the  volume  of  the 
metal. 

r\ 


Fig.  7. 


MEASUREMENT  OF  AN  IRREGULAR  BODY       31 

In  reading  a  graduate,  place  the  eye  on  the  level  of  the 
lowest  point  of  the  curved  surface  and  record  this-  as  the 
height  of  the  water.  As  the  graduations  are  cubic  centi- 
meter's, and  as  an  error  of  1  cm.3  in  the  volume  that  we 
are  measuring  would  be  a  considerable  per  cent  of  error, 
therefore,  estimate  tenths  of  a  cubic  centimeter  as  nearly 
as  you  can. 

Make  the  readings  indicated  by  the  table  of  observations 
and  record  in  a  similar  tabular  form  near  the  top  of  the 
left-hand  page  of  note-book. 

OBSERVATIONS 

Reading  before  immersing  the  metal      .     .     .          cm? 
Reading  after  immersing  the  metal  ....  cm.B 

Number  of  lump  of  metal  ....... 

Material  of  lump     ......... 


On  the  left-hand  page  of  the  note-book,  make  from 
your  apparatus,  outline  drawings  similar  to  Fig.  7,  and 
write  a  simple  description  of  the  experimental  method 
used. 

Discussion  : 

What  property  of  matter  makes  possible  this  method 
of  finding  the  volume  ? 

Conclusion  : 

Volume  of  lump  of  metal  No.  _____  is  _____  cm.8—  ______ 

cm.8  =  ._  ...cm.8. 


32  LABORATORY  EXERCISES 

EXPERIMENT   5 

Density 

OBJECT.    To  determine  the  density  of  wood  and  of  metal. 

APPARATUS.  Block  used  in  Experiment  3 ;  lump  of  metal 
used  in  Experiment  4 ;  spring  balance  or  other  balance ;  linen 
thread. 

Introductory : 

Iron  is  heavier  than  wood  and  lead  is  heavier  than  iron. 
By  this  we  mean  that,  if  we  take  pieces  of  the  three 
materials  of  the  same  size,  the  lead  has  the  greatest 
weight,  and  so  we  conclude  there  are  more  pounds  per 
cubic  foot  (or  grains  per  cubic  centimeter)  of  lead  than  of 
iron  or  of  wood.  That  is,  the  lead  has  the  greatest  den- 
sity, for  density  is  the  mass  per  unit  volume  of  a  sub- 
stance. In  the  metric  system  this  is  written  grams  per 

cubic  centimeter  or    ^'  . 
cm.** 

Experimental : 

All  that  is  necessary  for  the  calcu- 
lations is  to  know  the  mass  and  vol- 
ume. The  volume  of  each  of  the  solids 
to  be  used  has  already  been  obtained 
in  Experiments  3  and  4. 

The  mass  of  a  body  is  measured  by 
its  weight.  The  greater  the  mass,  the 
more  a  body  will  stretch  a  spring  from 
which  it  is  hung.  The  graduations  on 
the  scale  of  the  spring  balance  indicate 
the  masses  that  must  be  hung  upon 
Fig.  8.  the  hook,  in  order  to  pull  the  pointer 


DENSITY  33 

to  each  division  on  the  scale.  The  mass  of  the  block  may 
be  found,  then,  by  hanging  it  upon  a  spring  balance. 
Read  the  balance  to  tenths  of  the  smallest  division. 

If  a  beam  or  a  platform  balance  is  used,  read  on  page 
11  or  on  page  9  the  directions  for  its  use  before  perform- 
ing this  experiment. 

OBSERVATIONS 

Mass  of  wood g. 

Mass  of  metal g. 

From  your  apparatus  make,  on  the  left-hand  page  of  the 
note-book,  an  outline  drawing  like  Fig.  8.  On  the  same 
page  write  a  simple  description  of  what  you  did. 

Make  the  calculations  and  put  the  results  in  a  table  at 
the  top  of  the  right-hand  page  of  the  note-book. 

CALCULATED  RESULTS 

Volume  of  block  (from  Exp.  3)       ....          cm* 
Volume  of  metal  (from  Exp.  4)       ....  cm? 

Density  of  wood g.  per  cm? 

Density  of  metal  ( ) g.  per  cm? 

Conclusion : 

The  density  of  wood  is 

The  density  of is 

(name  metal) 


34  LABORATORY  EXERCISES 

EXPERIMENT   6 

Elasticity  — Hooke's  Law 

OBJECT.    To  find  the  relation  between  the  elongation  of  a  spiral 
spring  and  the  stretching  force,  provided  the  elastic  limit  is  not  ex- 


APPARATUS.  A  closely  coiled  spiral  about  10  cm.  long  and 
1.7  cm.  in  diameter,  made  of  $20  spring  brass  wire,  with  a  hook 
and  pointer  at  one  end  and  at  the  other  a  straight  section  for 
hanging  or  clamping  ;  stand  with  pendulum  clamp  and  meter  stick 
clamp  ;  meter  stick ;  pan  for  suspension  ;  metric  weights.1 

Introductory : 

When  a  steamboat  makes  its  landing,  the  large  hawsers 
tighten  as  the  boat  is  swung  toward  the  wharf.  The 
diameter  of  the  large  rope  becomes  smaller  and  measure- 
ments would  show  the  length  had  been  stretched.  The 
stretching  force  has  changed  both  the  shape  and  volume 
of  the  rope.  When  the  the  line  is  cast  off  again,  the  rope, 
because  it  is  an  elastic  body,  recovers  very  nearly  its  origi- 
nal diameter  and  length.  Sometimes  the  stretching  force 
is  so  great  that  the  rope  snaps  because  the  ultimate  strength 
of  the  rope  has  been  exceeded. 

In  materials  subjected  to  stretching  forces,  as  the  wire  in 
the  coil  of  a  spring  balance,  the  change  in  diameter  is  very 
slight,  but  there  is  considerable  lengthening  or  elongation. 
The  question  arises  whether  the  elongation  proceeds  irregu- 
larly or  at  a  uniform  rate  as  the  stretching  force  increases, 
provided  the  elastic  limit  of  the  material  is  not  exceeded. 

1  The  spiral  coil  may  be  conveniently  made  by  winding  the  wire  around 
a  \"  pipe.  The  special  pendulum  and  meter  sticlj:  clamps  may  be  replaced 
with  ordinary  laboratory  clamps  or  other  attachments.  In  case  weights 
heavier  than  those  specified"  for  the  loads  are  used,  a  larger  size  of  wire 
should  be  selected. 


ELASTICITY -HOOKE'S  LAW 


35 


Experimental : 

Place  the  meter  stick  in  a  vertical  position, 
the  weight  pan  on  the  hook  of  the  spring 
and  attach  the  pointer  just  above  the 
hook  at  right  angles  to  the  spring.  Sus- 
pend the  spring  so  that  the  end  of  the 
pointer  is  close  to  the  metric  scale,  but 
does  not  touch  it.  Also  try  to  adjust  the 
position  of  the  spring  so  that  the  pointer 
is  opposite  some  main  division  of  the  metric 
scale  such  as  the  10-cm.  or  20-cm.  mark. 
This  mark  is  the  zero  reading  or  the 
point  from  which  the  first  elongation  is  to 
be  measured.  Record  this  zero  reading. 

Put  a  5-gram  weight  in  the  pan  and 
read  the  position  of  the  pointer.  Take 
off  this  weight  and  allow  the  spring  to 
go  back.  Again  read  the  position  of  the 
pointer.  Now  put  on  the  10-gram  weight. 

OBSERVATIONS 


Suspend 


Fig.  9. 

Continue  in 


LOAD  ON  PAN 

READING  or 
POINTER 

ZERO  READING 

CORRECTED  KEADINO 
(TOTAL  ELONGATION) 

5  grams 

cm. 

cm. 

cm. 

10  grams 

cm. 

cm. 

cm. 

15  grams 

cm. 

cm. 

cm. 

20  grams 

cm. 

cm. 

cm. 

25  grams 

cm. 

cm. 

cm. 

30  grams 

cm. 

cm. 

cm. 

35  grams 

cm. 

cm. 

cm. 

40  grams 

cm. 

cm. 

cm. 

45  grams 

cm. 

cm. 

cm. 

HO  Drains 

cm. 

cm. 

cm. 

55  grams 

cm. 

cm. 

cm. 

60  grams 

cm. 

cm. 

cm. 

36  LABORATORY  EXERCISES 

this  manner,  increasing  the  load  5  grams  at  a  time  and 
recording  the  results  in  tabular  form  near  the  top  of  the 
left-hand  page.  The  total  elongation  due  to  the  load  is 
the  difference  between  the  pointer  reading  and  the  zero 
reading  which  is  made  each  time. 

Make  a  drawing  from  your  apparatus,  and  write ~a  sim- 
ple description  of  the  experimental  method. 

Curve  on  Cross  Section  Paper.  With  the  loads  taken 
and  the  total  elongations  obtained,  plot  a  curve  on  cross 
section  paper,  placing  loads  on  the  perpendicular  axis  and 
total  elongations  on  the  horizontal  axis.  Attach  the  cross 
section  paper  by  one  edge  to  the  right-hand  page  of  note- 
book. 

Discussion : 

What  kind  of  a  curve  is  obtained  ?  What  relation  does 
this  show  between  the  total  elongation  and  the  stretching 
force  ?  How  elastic  should  the  spring  be  in  order  to  obtain 
very  exact  results  ?  Was  your  spring  such  a  spring  ? 
What  is  the  principle  upon  which  a  spring  balance  works  ? 

Conclusion : 

Complete  the  following  statement  of  Hooke's  Law : 
When  the  elastic  limit  is  not  exceeded,  the  distortion  of 

a   bod)7   due   to   a   stretching   force  is to   the 

.  force. 


TENACITY  OF  WIRE  37 

EXPERIMENT    7 

Tenacity  of  Wire 

OBJECT.  To  determine  (a)  the  relation  between  the  tension 
and  the  elongation  of  a  wire;  (6)  the  comparative  tenacity  of 
copper,  iron,  and  brass. 

APPARATUS.  Block  for  clamping  wire ;  pulley  with  stem ; 
thumb  tacks  ;  weight  carrier;  slotted  weights — •  1  lb.,  2  lb.,  2  lb., 
5  lb.,  '0  lb.;  millimeter  scale  ;  large-sized  needle  ;  magnifier  (a 
cheap  convex  lens  may  be  used). 

MATERIAL.  Spools  of  iron,  brass,  and  copper  wire,  ft  28; 
sealing  wax. 

Introductory : 

When  a  load  is  suspended  by  means  of  a  cord,  the  cord 
stretches.  As  the  suspended  weight  is  increased,  the  cord 
stretches  further  until  it  finally  breaks.  A  wire  or  a  metal 
rod  behaves  in  the  same  way,  but  the  elongation  is  smaller 
and  not  so  readily  noticed.  There  is,  however,  definite 
elongation.  This  must  be  allowed  for  in  the  construction 
of  bridges  and  other  structures.  By  experimenting  with 
fine  wire  under  increasing  loads,  we  can  follow  all  the 
changes  until  the  wire  breaks. 


,JL,  0.    41      .. 

\   _ 

Urg 

S-T.   ///           ^^               p^lM 

1      Cf-] 

^ 

(                             jf  f 

1     r> 

1 

Fig.  10. 

20651- 


38 


LABORATORY  EXERCISES 


Experimental : 

(a)  The  block  is  clamped  to  one  end  of  the  laboratory 
table  and  the  stem  of  the  pulley  set  into  a  hole  bored 
diagonally  into  the  opposite  end. 

A  piece  of  wire  about  30  cm.  longer  than  the  table  is  cut 
off.  This  is  clamped  to  the  binding  post,  given  a  turn  around 
the  wooden  cylinder,  and  attached  to  the  weight  carrier  at 
the  other  end.  Care  must  be  taken  that  there  are  no  kinks 
or  sharp  bends  anywhere  in  the  wire.  The  wire  is  then 
placed  over  the  pulley  and  the  needle  attached  at  right  an- 
gles to  it  with  a  drop  of  melted  wax  at  a  point  near  the  pulley. 

The  millimeter  scale  is  then  fixed  in  place  beneath  the 
the  needle  with  the  thumb  tacks  so  that  its  divisions  are 
parallel  to  the  needle. 

A  2-lb.  weight  is  next  placed  on  the  carrier  to  straighten 
the  wire  ;  then  it  is  removed  and  the  zero  reading  of  the 
needle  taken,  tenths  of  the  smallest  scale  division  being 
estimated.  A  lens  may  be  used  to  advantage  in  estimating 
tenths. 

Weights  are  now  added,  a  pound  at  a  time,  the  amount 
of  stretching  force  and  the  reading  of  the  needle  on  the 
scale  being  noted  and  immediately  recorded  in  tabular 
form  near  the  top  of  the  left-hand  page. 

After  each  reading  remove  the  weights  and  again  note 
the  zero  reading.  The  force  which  causes  the  first  con- 
siderable shifting  in  the  zero  point  is  known  as  the  elastic 
limit.  Continue  the  readings  until  the  wire  breaks. 


OBSERVATIONS  ON 


WIRE,  GAUGE  No. 


STEETCHISO  FORCE 


etc. 


ZERO  READING 


ete. 


HEADING  OF  POINTER   BREAKING  STRENGTH 


etc. 


etc. 


TENACITY  OF  WIRE  39 

(6)  Replace  the  broken  wire  with  another  of  different 
material,  and  add  the  weights  one  pound  at  a  time  until 
the  wire  breaks,  without  recording  the  elongations.  Re- 
peat with  as  many  wires  as  the  instructor  may  designate. 
Record  results  in  tabular  form  on  the  second  left-hand 
page. 

OBSERVATIONS,  PART  (6) 


MATERIAL  or  WIRE 

GAUGE  NUMBER 

BREAKING  STRENGTH 



•        



On  the  left-hand  page  of  the  note-book  make  a  simple 
drawing  of  your  apparatus,  and  write  a  simple  description 
of  how  the  experiment  was  done. 

On  the  right-hand  page,  at  the  top,  place  the  calculated 
results  for  Part  (a)  in  tabular  form. 

CALCULATED  RESULTS 

Stretching  force           1  Ib.              2  Ib.             3  lb.,  etc. 

Elongation  ......mm.     mm.     mm.,  etc. 

Curve.  —  On  a  piece  of  cross  section  paper,  plot  a 
curve,  laying  off  forces  as  abscissae  (horizontal)  and 
elongations  as  ordinates  (vertical)  to  the  scale  given  by 
the  instructor.  Compare  the  force  at  the  point  where  the 
curve  begins  to  turn  with  the  elastic  limit.  Paste  the  cross 
section  paper  by  one  edge  into  the  note-book. 

Discussion : 

Does  the  wire  follow  Hooke's  Law  in  that  "the  dis- 
tortion (elorgation)  is  proportional  to  the  stretching 
force,"  through  any  part  of  the  test  as  shown  by  the 
curve  ?  If  so,  up  to  what  point  ? 


40  LABORATORY  EXERCISES 

Conclusion : 

(1)  State   the   relation  between  the  tension  of  a  wire 
and  its  elongation  (a)  up  to  the  elastic  limit,  (5)  beyond 
the  elastic  limit. 

(2)  Arrange  the  materials  tested  in  the  order  of  their 
tensile  strength,  placing  the  strongest  first. 

EXPERIMENT   8 

Relation  between  Pressure  and  Depth 

OBJECT.  — To  find  the  relation  between  the  depth  of  a  sub- 
merged surface  and  the  pressure  upon  it. 

APPARATUS.1  A  test  tube  loaded  with  shot,  upon  which 
melted  paraffin  has  been  poured,  so  that  the  tube  will  float 
vertically ;  a  paper  centimeter  scale,  attached  vertically  to  the 
inside  of  the  tube  with  paraffin;  weights — 1  to  10  grams  if 
a  6"  x  f"  test  tube  is  used  and  5  to  20  grams  if  a  8"  x  1"  test 
tube  is  used  ;  battery  jar  or  hydrometer  jar ;  cross  section  paper. 

Introductory : 

When  a  stick  is  thrown  endwise  into  water,  it  springs 
back  into  the  air.  When  a  boat  floats  in  water,  there 
must  be  an  upward  pressure  of  the  water  on  it  to  balance 
its  weight.  When  more  heavily  loaded,  it  sinks  more 
deeply,  but  the  upward  pressure  must  then  also  balance  its 
weight. 

Experimental : 

A  glass  tube  loaded  so  that  it  will  remain  upright  will 
be  floated  in  a  jar  of  water.  A  scale  on  the  inside  of 
the  tube  will  be  used  to  measure  changes  in  depth.  This 

1  The  method  of  this  experiment  was  called  to  our  attention  by 
Dr.  H.  C.  Cheston  of  the  High  School  of  Commerce,  New  York  City. 


RELATION  BETWEEN  PRESSURE  AND  DEPTH     41 


--:.-- 


tube  should  float  freely  and  should  not  be  allowed  to 
touch  the  sides  of  the  jar.  The  scale  readings  are 
taken  by  sighting  through 
the  jar  along  the  under  side 
of  the  water  surface.  By  add- 
ing small  weights  as  indicated 
in  the  table  below,  the  level 
of  the  bottom  of  the  tube 
may  be  changed.  By  compar- 
ing the  changes  in  depth  and 
the  changees  in  weight  pro- 
ducing them,  we  may  find  how 
the  upward  pressure  of  the  water 
(which  balances  the  weight 
of  the  tube)  varies  with  the 
depth  of  the  surface  on  which 
it  acts.  Fi^n- 

Place  your  observations  in  a  table  near  the  top  of  the 
left-hand  page. 


NUMBER  or 

OBSERVATION 

1 


OBSERVATIONS 

WEIGHT 

Loaded  tube  alone  ..... 

Loaded  tube  alone  +    2  grams  . 

Loaded  tube  alone  +    4  grams  . 

Loaded  tube  alone  +    6  grams  . 

Loaded  tube  alone  +    8  grams  . 

Loaded  tube  alone  +  10  grams  . 


SCALB 

READING 


cm. 
cm. 
cm. 
cm. 
cm. 


Make  a  drawing  from  your  apparatus  and  write  a  simple 
description  of  the  method  of  the  experiment. 

Make  the  following  tabulations  at  the  top  of  the  right- 
hand  page: 


42  LABORATORY  EXERCISES 


NUMBERS 


CALCULATED  RESULTS 

CHANGE  OP  CHANGE  01 


PRESSURE  DEPTH 

1  —  2 grams  ....  cm. 

1  —  3 grams  ....  cm. 

1 — 4 grams  ....  cm. 

1 — 5  .    '.     .     .     .  grams  ....  cm. 

1  —  6 grams  ....  cm. 

Curve  on  Cross  Section  Paper.  — The  readings  of  change 
of  pressure  and  change  of  depth  should  be  plotted  on 
cross  section  paper,  depths  on  the  perpendicular  axis  and 
pressures  on  the  horizontal  axis.  Use  a  scale  of  5  small 
spaces  to  1  gram,  and  2  small  spaces  to  1  mm.  If  the 
resulting  graph  is  a  straight  line,  we  may  conclude  that 
twice  the  depth  was  caused  by  twice  the  pressure  and  so 
on,  or  that  the  pressure  is  directly  proportional  to  the 
depth.  Paste  the  cross  section  paper  by  one  edge  in  the 
note-book. 

Discussion : 

At  each  observation  in  the  experiment,  what  relation 
must  exist  between  the  total  weight  of  the  floating  tube 
and  the  upward  pressure  of  the  water?  Why  is  it  not 
necessary  to  consider  any  sidewise  pressures  that  may  be 
exerted  on  the  tube  ? 

Conclusion : 

What  is  the  relation  between  the  pressure  on  a  sub- 
merged surface  and  the  distance  of  that  surface  below  the 
surface  of  the  liquid  ? 


ARCHIMEDES'  PRINCIPLE  43 

EXPERIMENT   9 

Archimedes'  Principle 

OBJECT.  To  determine  the  relation  between  the  loss  of  weight 
of  a  sinking  solid  and  the  weight  of  a  liquid  displaced  by  it. 

APPARATUS.  Lump  of  coal  with  thread,  or  copper  wire  $22  at- 
tached ;  overflow  can  ;  catch  bucket  or  beaker  with  wire  loop  for 
suspension ;  spring  balance  (250  g.),  or  beam  balance  ;  battery  jar. 

Introductory : 

It  is  much  easier  to  lift  the  anchor  of  a  boat  when  the 
anchor  is  in  the  water  than  when  it  is  out  of  the  water. 
The  displaced  water  balances  part  of  the  weight  of  the 
anchor,  and  so  makes  it  seem  lighter,  because  the  upward 
pressure  of  the  water  on  the  bottom  of  the  anchor  is 
greater  than  the  downward  pressure  on  the  top.  The 
anchor  displaces  a  volume  of  water  its  own  size.  We  wish 
to  compare  the  loss  of  weight  of  a  body  submerged  in  a 
liquid  with  the  weight  of  the  liquid  displaced  by  it. 
This  was  first  done  by  Archimedes,  and  the  relation  found 
is  called  Archimedes'  Principle. 

Experimental : 

Use  a  piece  of  coal  for  the  solid.  By  weighing  it 
in  air,  with  a  spring  balance,  and  then  when  immersed  in 
water  in  a  jar,  the  loss  in  weight  of  the  lump  can  be  found. 

When  a  can  with  a  spout,  called  an  overflow  can,  is  rilled 
and  placed  on  a  level  table,  the  water  will  run  out  to  the 
level  of  the  spout.  By  placing  a  weighed  beaker  under 
the  spout  and  carefully  lowering  the  coal  into  the  can, 
the  water  which  overflows  may  be  caught  and  weighed. 
Comparing  the  weight  of  this  displaced  water  with  the 
loss  of  weight  of  the  coal,  will  give  the  relation  sought. 


44 


LABORATORY  EXERCISES 


Record  the  following  readings  in  tabular  form  near  the 
top  of  the  left-hand  page  : 


OBSERVATIONS 

Weight  of  coal  in  air       , 

Weight  of  coal  in  water 

Weight  of  catch  bucket 

Weight  of  catch  bucket  +  displaced  ivater 


Briefly  describe  what  you  did,  illustrating  each  step 
with  a  drawing  from  your  apparatus,  similar  to  Fig.  12 
(A,  B,  and  (7). 


B 

A 


1 

T 

* 

jBfCK 

G^f 

\;^;~  :=-:i? 

r—r^rirrij 

^jin-rtRr 

c 

3 

r                      -4 

—  zq 

Fig.  12. 

CALCULATED  RESULTS 


Loss  of  weight  of  coal  in  water 
Weight  of  an  equal  volume  of  ivater 


Conclusion  : 

State  the  relation  between  the  loss  of  weight  of  a  sink- 
ing body  and  the  weight  of  a-liquid  displaced  by  it. 


LAW  OF  FLOTATION 


45 


EXPERIMENT   10 

Law  of  Flotation 

OBJECT.  —  To  determine  the  relation  between  the  weight  of  a 
floating  body  and  the  weight  of  a  liquid  displaced  by  it. 

APPARATUS.  Block  loaded  to  float  upright  on  water  ;  overflow 
can ;  catch  bucket  or  beaker  with  wire  loop  for  suspension ; 
spring  or  beam  balance. 

Introductory : 

The  cork  float  on  a  fishline  exerts  no  pull  on  the  line. 
The  weight  of  an  ocean  liner  is  supported  by  the  upward 
push  of  the  water.     A  boat  is  said  to  have  a  certain  num- 
ber  of   tons    displacement, 
depending  upon  its  size  and 
weight.     What  is  the  rela-       <*> 
tion   between   this   number 
of  tons  of  water  displaced 
and  the  weight  of  the  boat  ? 


Experimental : 

A  method  similar  to  that 
used  in  Experiment  9  will 
give  us  the  relation  between 
the  weight  of  the  wooden 
block  and  the  weight  of  the 
liquid  displaced  by  it.  Place  the  table  of  observations 
near  the  top  of  the  left-hand  page. 


Fig.  13. 


OBSERVATIONS 

Weight  of  block 

Weight  of  catch  bucket^  empty    . 

Weight  of  catch  bucket  +  displaced  water 


46  LABORATORY  EXERCISES 

Write  a  simple  description  of  the  steps  in  the  expert 
ment,  illustrating  each  with  a  drawing  from  your  apparatus. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 
Weight  of  water  displaced  by  floating  body     .     .         g. 

f      •  z,   {floating  body   ....         g. 
Comparison  of  weights  \ , .    7       , 

i  displaced  water    ...         g. 

Conclusion : 

The  weight  of  a  floating  body  and  the  weight  of  the 
liquid  displaced  by  it  are  . 


EXPERIMENT  10  (Alternative) 

Law  of  Flotation 

OBJECT.  To  determine  the  relation  between  the  weight  of  a 
floating  body  and  the  weight  of  the  liquid  displaced  by  it. 

APPARATUS.  A  wooden  bar  20  cm.  long  and  1  cm.  square 
with  metric  scale  attached  and  loaded  so  as  to  be  almost  sub- 
merged when  floating  upright  in  water;1  hydrometer  jar  or 
battery  jar ;  platform  balance ;  metric  weights. 

Introductory : 

The  cork  float  on  a  fishline  exerts  no  pull  on  the  line. 
The  weight  of  an  ocean  liner  is  supported  by  the  upward 
push  of  the  water.  A  boat  is  said  to  have  a  certain  num- 
ber of  tons  displacement,  depending  upon  its  size  and 

1  The  ordinary  wooden  hydrometer  can  be  made  available  by  drilling 
a  hole  in  the  lower  end,  adding  lead  shot,  and  closing  with  a  cork  plug. 
The  weight  of  the  bar  should  be  so  adjusted  that  the  bar  will  float  almost 
submerged.  Finally  put  a  light  coat  of  paraffin  over  the  end  which  was 
opened. 


LAW  OF  FLOTATION  47 

weight.     What  is  the  relation   between  this   number  of 
tons  of  water  displaced  and  the  weight  of  the  boat  ? 

Experimental : 

The  wooden  bar  is  to  be  weighed  and  then  floated  in 
the  water  of  jar  so  as  to  note  the  depth  to  which 
it  is  submerged.  The  metric  scale  on  the  bar 
gives  the  length  of  the  column  of  water  dis- 
placed and,  like  the  bar  the  column  of  displaced 
water,  is  1  centimeter  square.  Therefore  the 
reading  on  the  metric  scale  is  numerically  equal 
to  the  number  of  cubic  centimeters  of  displaced 
water.  Since  a  cubic  centimeter  of  water  at 
ordinary  temperatures  weighs  approximately  a 
gram,  the  weight  of  the  displaced  water  can  eas- 
ily be  found.  A  comparison  of  the  weight  of  the 
floating  bar  and  the  weight  of  the  displaced  Fig.  14. 
water  will  bring  out  the  principle  of  flotation. 

OBSERVATIONS 


Weight  of  bar g. 

Length  of  column  of  displaced  water     .     .     .  cm. 

Make  a  drawing  of  the  floating  bar  from  your  apparatus 
and  write  a  simple  description  of  the  experimental  method. 

CALCULATED  RESULTS 

Volume  of  water  displaced  by  floating  body    .          cm.* 
Weight  of  water  displaced  by  floating  body     .  g. 

\  floating  body      .     .          g. 
Comparison  of  weights   <    ,.    7       ,       . 

[  displaced  water .     .          g. 

Conclusion : 

The  weight  of  a  floating  body  and  the  weight  of  the 
liquid  displaced  by  it  are . 


48 


LABORATORY  EXERCISES 


EXPERIMENT    11 

Specific  Gravity  of  Solids 

OBJECT.    To  find  the  specific  gravity  of  various  solids. 

APPARATUS.  Spring  balance,  or  beam  balance  arranged  for 
weighing  in  water  ;  battery  jar  ;  pieces  of  coal,  glass,  and  marble, 
or  other  solids  desired. 

Introductory: 

Lead  is  a  very  heavy  metal.  While  a  pailful  of  water 
weighs  only  about  20  pounds,  the  weight  in  pieces  of  lead 
that  would  just  fill  the  pail  would  be  about  225  pounds. 
Lead  weighs  about  11.2  times  as  much  as  the  same  volume 

of  water.  We  say  that 
the  "  specific  gravity  " 
of  lead  is  11.2  times. 
The  specific  gravity  of 
a  substance  is  the  num- 
ber of  times  a  piece  of 
the  substance  is  as 
heavy  as  the  same  vol- 
ume of  water. 

Experimental : 

It  will  be  necessary 
to  get  the  weight  of  a 
lump  of  coal  and  the 
weight  of  the  same  vol- 
ume of  water.  The 

weight  of  the  coal  can  be  found  directly  with  a  spring 
balance,  and  Archimedes'  Principle  will  help  us  in  getting 
the  weight  of  an  equal  volume  of  water.  If  the  coal  is 
weighed  while  immersed  in  water,  it  will  weigh  less  than 


A 

A 

B 
J^ 

T 

I 

/^  ,  

) 

..( 

± 

} 

— 





Fig.  15. 


SPECIFIC   GRAVITY  OF  SOLIDS 


49 


in  air  by  an  amount  equal  to  the  weight  of  water  having 
the  same  size  (volume)  as  the  coal.  The  specific  gravity 
of  the  other  solids  furnished  may  be  found  in  the  same 
way. 

Record  the  weighings  in  tabular  form  near  the  top  of 
the  left-hand  page. 

OBSERVATIONS 


COAL 

MAKBLK 

GLASS 

Weight  of  body  in  air    .     . 
Weight  of  body  in  water    . 

Then  make  drawings  from  your  apparatus  and  write  a 
simple  description  of  how  the  experiment  was  done. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 


COAL 

MARBLE 

GLASS 

Weight  of  water  size  of  solid  . 
Weight  of  solid      
Specific  gravity  of  solid       .     . 

Conclusion : 

The  specific  gravity  of  coal  is times;  the  specific 

gravity  of  marble  is times;    the  specific  gravity  of 

glass  is times. 


50 


LABORATORY  EXERCISES 


EXPERIMENT   12 

Specific  Gravity  of  a  Liquid 
(Bottle  Method) 

OBJECT.  To  obtain  the  specific  gravity  of  a  solution  of  copper 
sulphate  with  a  specific  gravity  bottle. 

APPARATUS.  Specific  gravity  bottle  ;  spring  balance  (250  g.) 
with  scale  pan,  or  beam  balance  ;  bottle  or  jar  of  copper  sulphate 
solution  provided  with  a  siphon  delivery  tube,  ending  with  rubber 
connection,  pinchcock,  and  glass  jet  tube  (Fig.  17). 

MATERIAL.  Water;  saturated  solution  of  copper  sulphate;1  small 
cloths  for  wiping. 


Introductory : 

If  we  find  the  weight  of  a 
gallon  of  water  and  of  a  gallon 
of  alcohol,  we  can  directly  deter- 
mine the  specific  gravity  of  the 
alcohol  by  finding  how  many 
times  it  is  as  heavy  as  water. 
This  is  a  general 
method  for  finding 
the  specific  gravity 
of  any  liquid. 


Experimental : 

We  use  small  spe- 
cific   gravity    bottles 
having  perforated  glass  stoppers,  as  in  this  way  we  can 


Fig.  16. 


Fig.  17.     Jar  and  siphon  for 
solution. 


1  A  hot  saturated  solution  should  be  made  and  allowed  to  cool,  or  a 
cheesecloth  bag  full  of  copper  sulphate  crystals  should  be  suspended  in 
the  top  of  a  jar  of  water  and  allowed  to  stand  at  least  twenty-four  hours, 
or  until  no  more  copper  sulphate  will  dissolve. 


SPECIFIC  GRAVITY  OF  A  LIQUID  51 

obtain  very  exactly  equal  volumes  of  the  two  liquids. 
The  weight  of  the  specific  gravity  bottle  must  first  be 
found.  Then  it  is  to  be  weighed  full  of  water  and  next 
full  of  copper  sulphate  solution.  By  comparing  the  weight 
of  the  copper  sulphate  solution  filling  the  bottle  with  the 
weight  of  the  water  filling  the  same  space,  the  specific 
gravity  of  the  copper  sulphate  solution  may  be  found. 

CAUTION.  Using  the  wiping  cloths  if  necessary,  see  that  the 
bottle  is  dry  on  the  outside  before  weighing  and  avoid  handling  it 
except  by  the  neck,  for  the  heat  of  the  hand  is  likely  to  drive  out 
some  of  the  liquid  through  the  stopper,  after  it  has  been  fitted.  After 
the  water  weighed  has  been  emptied  out,  rinse  the  bottle  with  a  little 
of  the  sulphate  solution. 

Record  the  weighings  in  tabular  form  near  the  top  of 
the  left-hand  page. 

OBSERVATIONS 

Weight  of  scale  pan  and  empty  bottle  ....  g. 
Weight  of  pan  and  bottle  fitted  with  water     .     .  g. 
Weight  of  pan  and  bottle  filled  with  copper  sul- 
phate solution g. 

Make  drawings  from  your  apparatus  and  write  a  short 
description  of  how  the  experiment  was  done. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 

Weight  of  water  filling  bottle g. 

Weight  of  copper  sulphate  solution  filling  bottle  .          g. 
Specific  gravity  of  copper  sulphate  solution   .     .         times 

Conclusion : 

The  specific  gravity  of  copper  sulphate  solution  is 

times. 


52  LABORATORY  EXERCISES 

EXPERIMENT    13 

Specific  Gravity  of  a  Liquid 
(Hydrometer  Method) 

OBJECT.  To  find  the  specific  gravity  of  a  copper  sulphate  solu- 
tion by  the  hydrometer  method. 

APPARATUS.  Hydrometer  jars ;  square  wooden  hydrometer 
graduated  in  millimeters;  glass  hydrometer  for  heavy  liquids 
(1  to  2). 

MATERIAL.  Water ;  saturated  solution  of  copper  sulphate  as 
in  Experiment  12. 

Introductory: 

A  boat,  passing  from  fresh  water  into  the  ocean,  rises 
a  little,  as  the  boat  displaces  its  own  weight  in  each 
case,  and  the  salt  water,  being  more  dense,  has  less  volume 
for  the  same  weight.  An  electric  light  bulb  in  concen- 
trated sulphuric  acid  floated  with  100  c.c.  of  its  volume 
submerged  ;  in  alcohol,  which  is  half  as  dense  as  sulphuric 
acid,  the  same  bulb  would  sink  until  200  c.c.  were  sub- 
merged. We  see,  then,  that  the  greater  the  specific  gravity 
of  a  liquid  the  less  portion  of  a  given  floating  body  will  be 
submerged  in  it.  More  exactly,  the  volumes  of  a  floating 
body  submerged  in  two  liquids  are  inversely  proportional 
to  the  specific  gravities  of  the  two  liquids. 

Experimental : 

(a)  A  graduated  float  used  for  obtaining  the  specific 
gravity  of  liquids  is  called  an  hydrometer.  The  hydrom- 
eter to  be  used  is  a  loaded  stick  1  cm.  square  and  graduated 
in  centimeters  and  tenths.  If  we  now  immerse  this  in 
water  (Fig.  18)  and  record  the  depth  to  which  it  sinks, 
and  then  do  the  same  with  a  copper  sulphate  solution 


SPECIFIC  GRAVITY  OF  A  LIQUID 


53 


(Fig.  19),  the  hydrometer  will  sink  deeper  in  the  less 
dense  liquid.  The  volume  of  each  liquid  displaced  may 
be  measured  by  the  depth  of  the  submerged  part  of  the 
hydrometer,  since  each  centimeter  of  length  means  1  c.c. 
of  volume.  If,  then,  we  divide  the  length  submerged  in 
in  water  by  the  length  submerged  in  copper  sulphate,  we 
shall  obtain  the  specific  gravity  of  the  copper  sulphate 
solution. 


Fig.  18. 


Fig.  19. 


Fig.  20. 


(J)  Direct-reading  hydrometers  are  made  of  glass  tubes 
loaded  so  as  to  float  upright  and  provided  with  a  scale 
which  gives  the  specific  gravity  directly  (Fig.  20).  After 
completing  calculations  on  part  (a),  ask  the  instructor 
for  such  a  hydrometer,  and  with  it  find  the  specific  gravity 
of  your  solution,  as  a  check  on  your  results.  Record  the 
observations  in  tabular  form  near  the  top  of  the  left-hand 


OBSERVATIONS 

Reading  of  bar  in  water 

Reading  of  bar  in  copper  sulphate  solution 
Reading  of  glass  hydrometer  in  copper  sulphate 
solution  .... 


cm. 
cm. 


54  LABORATORY  EXERCISES 

Make  drawings  from  your  apparatus  showing  the  posi 
tion  of  the  wooden  hydrometer  in  the  two  liquids  and 
the  position  of  th*e  glass  hydrometer  in  the  copper  sulphate 
solution.  Accompany  these  drawings  with  a  short  de- 
scription of  the  method  of  work. 

CALCULATED  RESULT 

Specific  gravity  of  copper  sulphate  solution 

as  determined  by  wooden  hydrometer    .     .  times 

Discussion : 

Explain  why  the  volume  of  water  displaced  was  divided 
by  the  volume  of  copper  sulphate  solution  displaced. 

Conclusion : 

The  specific  gravity  of  the  copper  sulphate  solution 
by  this  method  (wooden  hydrometer)  is  --    -  times 

by  the  bottle  method  (Experiment  12)  is times 

by  the  direct  reading  of  the  glass  hydrom- 
eter is  times 


SPECIFIC  GRAVITY  OF  A  LIQUID  55 

EXPERIMENT   14 

Specific  Gravity  of  a  Liquid 
(Hare's  Method) 

OBJECT.  To  find  the  specific  gravity  of  alcohol  and  of  a  salt 
solution  by  Hare's  method. 

APPARATUS.  Two  90  cm.  lengths  of  \"  glass  tubing ;  lead  or 
glass  T-tube,  or  Y-tube ;  2  rubber  connections ;  black  rubber 
tubing  of  length  convenient  for  suction  ;  screw  compressor ;  ring 
stand  and  clamp  for  supporting  T-tube  or  Y-tube ;  2  tumblers 
(preferably  of  thin  glass  and  with  nearly  vertical  sides),  or  2 
oeakers. 

MATERIAL.  Distilled  water,  if  available  ;  saturated  solution  of 
common  salt,  and  grain  alcohol  in  stock  bottles  provided  with 
siphon  tubes  about  -£$"  bore. 

Introductory : 

The  simple  barometer  is  nothing  more  than  a  long  tube, 
closed  at  one  end  and  filled  with  mercury,  which  is  then 
inverted  in  a  dish  of  mercury.  A  mercury  column  about 
76  centimeters  in  length  remains  standing  in  the  tube. 
This  column  is  held  up  by  the  pressure  of  the  atmosphere. 
It  has  also  been  determined  experimentally  that  the 
pressure  of  the  air  supports  a  much  longer  column  of 
water  —  approximately  34  feet.  We  know  that  mercury, 
volume  for  volume,  is  much  heavier  than  water,  or,  as  we 
say,  has  a  greater  specific  gravity.  The  fact  that  the 
atmosphere  holds  up  columns  of  liquid  whose  length  varies 
with  the  particular  liquid  taken,  has  been  utilized  in  an 
ingenious  method  for  determining  the  specific  gravity  of 
liquids. 


56 


LABORATORY  EXERCISES 


Experimental : 

The  apparatus  (Fig.  21)  consists  of  two  long  parallel 
tubes  with  their  lower  ends  dipping  into  tumblers  of 
liquids.  The  upper  end  of  each 
is  joined  by  a  rubber  connection 
to  an  arm  of  a  T-tube.  To  the 
center  tube  of  the  T  is  attached  a 
rubber  tube  to  be  used  for  suc- 
tion, which  can  be  closed  by  a 
screw  compressor. 

(a)  Half-  fill  one  tumbler  with 
water  and  the  other  with  a  sat- 
urated solution  of  salt. 

With  the  rubber  tubing  open, 
compare  the  water  levels  inside 
and  outside  the  long  tube.  Ac- 
count for  this  condition  of  levels. 
Is  it  also  true  for  th'e  levels  of  the 
salt  solution  ? 

Suck  out  a  little  air  through 
the  rubber  tube,  noting  the  be- 
havior of  the  liquids.  What  pres- 
sure causes  the  liquids  to  rise  in  the 
tubes  ? 

Again  remove  air  by  suction 
until  the  water  column  is  pushed 
up  nearly  to  the  top  of  its  tube. 
Pinch  the  rubber  tube  tightly  and 
close  the  screw  compressor.  Note 
the  relative  height  of  the  two  liq- 
uids. The  pressure  on  the  upper  surfaces  of  the  two 
liquids  is  the  same.  How  does  this  pressure  compare  with 
the  outside  air  pressure  ?  What  pressure  forced  the  liquids 


Fig  21. 


SPECIFIC  GRAVITY  OF  A  LIQUID  57 

up  into  the  tubes  ?  How  does  this  pressure  compare  with  the 
downward  pressure  of  each  liquid?  Compare,  then,  the 
downward  pressure  of  the  water  column  with  that  of  the  salt 
solution. 

Measure  with  a  meter  stick  the  length  of  the  water 
column  above  the  level  of  the  water  in  the  tumbler. 
Obtain  similarly  the  length  of  the  column  of  the  salt 
solution.  Record  the  measurements  in  tabular  form  near 
the  top  of  the  left-hand  page. 

(5)  Open  the  compressor  and  allow  the  liquids  to  run 
back  into  their  tumblers.  Return  the  salt  solution  to  its 
stock  bottle  and  rinse  out  the  tumbler.  Detach  the  long 
tube  used  for  the  salt  solution,  and,  after  washing,  attach 
it  again. 

Put  grain  alcohol  into  the  empty  tumbler  and  repeat 
the  experiment  so  as  to  obtain  the  length  of  the  water 
and  the  alcohol  columns,  taking  care  not  to  suck  the  alcohol 
up  into  the  mouth.  Tabulate  the  measurements  near  the 
top  of  the  left-hand  page. 

Return  the  alcohol  to  its  stock  bottle. 

OBSERVATIONS 
Part  (a)  : 

Length  of  the  water  column     .     .     .     .     .     .  cm. 

Length  of  the  salt  solution  column     ...»          cm. 
Part  (6)  : 

Length  of  the  water  column cm. 

Length  of  the  grain  alcohol  column  ....          cm. 

Make  an  outline  drawing  of  the  apparatus  used,  and 
write  a  simple  description  of  the  general  method  of  the 
experiment. 

With  the  water  and  the  salt  solution,  the  downward 
pressure  per  square  centimeter  of  each,  balances  the  same 
amount  of  atmospheric  pressure.  The  two  columns  must 


58  LABORATORY  EXERCISES 

then  have  the  same  weight.  Being  of  equal  cross  section, 
their  lengths  are  proportional  to  their  volumes.  But  the 
greater  the  specific  gravity  of  a  liquid,  the  smaller  the 
volume  for  a  given  weight.  Are  the  relative  weights, 
then,  directly  or  inversely  proportional  to  the  heights  of  the 
columns  ?  With  this  relation  in  mind,  calculate  the  spe- 
cific gravity  of  the  salt  solution  and  of  the  alcohol,  relative 
to  water.  Record  the  results  in  tabular  form  at  the  top 
of  the  right-hand  page. 

CALCULATED  RESULTS 

Specific  gravity  of  the  salt  solution    .     .    =       times 

Specific  gravity  of  the  alcohol  ....    =       times 

Discussion : 

Answer  under  this  heading  on  the  right-hand  page  the 
italicized  questions  occurring  in  the  directions. 

Conclusion : 

The  specific  gravity  of  the  salt  solution  is times ; 

the  specific  gravity  of  the  alcohol  is times. 


EXPERIMENT   14    (Alternative) 

Specific  Gravity  of  Liquids 

(Balancing  Columns) 

OBJECT.  To  find  the  specific  gravity  of  (a)  carbon  tetrachloride, 
(&)  grain  alcohol,  by  the  method  of  balancing  columns  in  a  U-tube. 

APPARATUS.  2  Mohr  burettes  (50  c.c.)  connected  by  a  piece 
of  thick-walled  rubber  tubing  of  sufficient  length  ;  Hofmann  screw 
compressor  ;  ring  stand  ;  two  burette  clamps  ;  2  glass  '  funnels, 
1\n ',  or  tops  of  two  thistle  tubes  ;  beaker;  medicine  dropper. 


SPECIFIC  GRAVITY  OF  LIQUIDS  59 

MATERIALS.  Mercury ;  distilled  water  if  available ;  carbon 
tetrachloride  ;  grain  alcohol.  (Other  liquids,  such  as  glycerine 
kerosene,  etc.,  as  the  instructor  desires.) 

Introductory : 

When  mercury  fills  the  lower  rounded  portion  of  a  U- 
tube,  the  mercury  stands  at  the  same  level  in  the  two 
arms,  since  the  downward  pressure  of  the  air  is  the  same 
on  the  two  mercury  surfaces. 

When  a  certain  volume  of  water  is  poured  into  one  arm 
of  this  same  tube,  and  an  equal  volume  of  kerosene  into 
the  other  arm,  the  mercury  level  in  the  water  arm  is 
lower  than  that  in  'the  kerosene  arm.  Since  the  mercury 
is  free  to  move,  the  given  volume  of  water  must  press 
down  with  greater  weight  on  the  mercury  than  does  the 
same  volume  of  kerosene.  Accordingly,  volume  for 
volume,  the  kerosene  weighs  less  than  the  water.  Usually 
the  specific  gravity  is  found  by  calculating  the  ratio  be- 
tween weights  of  equal  volumes.  Since  this  is  so,  might 
not  the  inverse  ratio  between  the  volumes  of  equal  weights 
give  the  specific  gravity  ? 

Experimental : 

As  we  have  seen,  equal  weights  may  be  measured  by 
the  downward  pressure  of  liquids.  The  equal  weights 
can  be  obtained  by  pouring  just  enough  of  each  liquid 
into  its  arm  of  the  U-tube,  so  as  to  make  the  two  mercury 
surfaces  stand  at  the  same  level.  All  that  remains  is  the 
measurement  of  the  volumes  of  the  two  liquids  and  the 
finding  of  the  ratio,  remembering  that  it  is  an  inverse 
one. 

Clamp  the  two  burettes  at  about  a  third  of  their  length 
from  their  lower  ends  and  in  a  vertical  parallel  position 
with  the  50-c.c.  marks  horizontally  opposite  each  other. 


60 


LABORATORY   EXERCISES 


Slip  the  screw  compressor   over   the   rubber   connecting 
tube  and  attach  the  ends  of  the  tube  to  the  burettes. 

Pour  mercury  through  a  thistle 
tube  top  or  funnel  at  the  top  of  one 
burette  until  the  mercury  surface 
in  each  burette  stands  at  the  50-c.c. 
graduation,  or  some  mark  a  short 
distance  above  (Fig.  22).  Squeeze 
out  the  air  bubbles  in  the  connect- 
ing tube  before  taking  the  zero 
reading  of  the  mercury  levels. 

(a)  Record  the  zero  reading  of 
the  burettes  in  the  table  of  obser- 
vations. Then  close  the  screw  com- 
pressor on  the  connecting  tube. 

Into  the  right-hand  burette  pour 
enough  carbon  tetrachloride  to  half 
fill  the  burette.  Add  about  the  same 
volume  of  water  to  the  other  burette. 
Cautiously  open  the  compressor  a  lit- 
tle, noting  whether  the  tetrachloride 
column  is  balanced  by  the  water. 
If  not,  close  the  compressor,  add 
more  water,  and  test  again.  Con- 
tinue in  this  manner  until  the  water 
balances  the  tetrachloride,  as  shown 
by  the  mercury  remaining  at  the 
same  levels  when  the  compressor  is 
opened  wide.  A  medicine  dropper 
Fi  22  ig  convenient  for  adding  the  last 

portions  of  water  needed. 

Read  and  record  the  top  levels  of  the  balancing  columns. 

Raise  the  tetrachloride  burette  so  that  the  mercury  just 

runs  into  the  connecting  tube.       Over  this  end  of  the  tube 


SPECIFIC  GRAVITY  OF  LIQUIDS  61 

close  the  screw  compressor  and  slip  off  the  rubber  tube,  so 
that  the  tetrachloride  can  empty  into  a  beaker  placed  below 
the  burette.  Pour  the  tetrachloride  into  its  stock  bottle. 

(6)  Rinse  out  the  open  burette  with  a  few  cubic  centi- 
meters of  alcohol  (or  other  liquid  to  be  used)  and  again 
connect  the  rubber  tube. 

Then  obtain  as  in  (a)  a  column  of  alcohol  which 
balances  the  water  column  in  the  left-hand  burette. 

Record  all  readings  in  a  tabular  form  near  the  top  of  the 
left-hand  page. 

OBSERVATIONS 
Part  O)  : 

Reading  of  mercury  levels cm.3 

Heading  at  top  of  water  column cm.3 

Reading  at  top  of  tetrachloride  column  .      .     .         cm.3 
Part  (6)  : 

Reading  of  mercury  levels cm.3 

Reading  at  top  of  water  column cm.3 

Reading  at  top  of  alcohol  column cm.3 

Make  an  outline  drawing  of  your  apparatus  and  de- 
scribe briefly  how  the  experiment  was  done. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page.  The  specific  gravities  are  to  be  calcu- 
lated with  reference  to  water. 

CALCULATED  RESULTS 

Part  (a)  : 

Volume  of  the  water  column cm.3 

Volume  of  tetrachloride  column cm.8 

Specific  gravity  of  tetrachloride   .     . =  times 

Part  (6)  : 

Volume  of  water  column cm.8 

Volume  of  alcohol  column cm.3 

Specific  gravity  of  alcohol  .... =  times 


62  LABORATORY   EXERCISES 

Discussion : 

Why  is  the  specific  gravity  in  this  experiment  the  in- 
verse ratio  of  the  volumes  of  the  balancing  columns  ? 

Conclusion : 

The   specific   gravity  of    carbon    tetrachloride    is 

times.     The  specific  gravity  of  alcohol  is times. 


EXPERIMENT   15 

Density  of  Air 

OBJECT.  To  determine  the  approximate  density  of  air  in  the 
room. 

APPARATUS:  Air  pump ;  round-bottom  flask  (250  c.c.)  with  a 
tightly  fitting  1-hole  rubber  stopper  carrying  a  glass  inlet  tube 
with  a  piece  of.  thick-walled  rubber  tubing  attached;  screw 
compressor  ;  beam  or  horn  pan  balance  weighing  to  0.01  gram  ; 
metric  weights  ;  graduate  ;  large  battery  jar,  or  pail. 

Introductory : 

It  is  very  evident  that  lead  has  weight.  Even  a  small 
child  knows  that  a  tumbler  of  water  is  heavier  than  the 
empty  glass.  We  know  that  solids  and  liquids  have 
weight,  but  does  the  air  which  surrounds  us  have  weight  ? 
If  balloons  are  lighter  than  air,  the  air  must  have  weight. 
It  would  be  interesting  to  find  out  just  how  dense  air  is, 
that  is,  the  number  of  grams  to  a  cubic  centimeter. 

Experimental : 

A  flask  may  be  weighed  full  of  air  and  then  the  air 
partially  pumped  out.  Then  the  exhausted  flask  may  be 
weighed.  The  difference  between  the  two  weights  is  the 
weight  of  air  pumped  out  of  the  flask.  The  volume  of 


DENSITY  OF  AIR 


63 


Fig.  23. 


this  air  may  be  found  by  measuring  the  water  which  will 
run  into  the  exhausted  flask.     With  the 
weight  and  volume  of  the  air  known,  the 
density  (grams  per  cubic  centimeter)  may 
be  found. 

Make  all  weighings  to  the  nearest  cen- 
tigram. In  all  weighings  of  the  flask,  in- 
clude the  rubber  stopper  with  its  tubing 
and  screw  compressor,  and  any  wire  sus- 
pension used  with  the  balance.  See  that 
all  joints  between  rubber  and  glass  are 
tight  before  exhaustion.  Allow  at  least 
live  minutes  for  the  exhaustion  of  the 
flask,  and  be  sure 
the  screw  compres- 
sor is  tightly  closed 
before  the  removal 
of  the  rubber  tube  from  the  pump. 
Immerse  most  of  the  flask  in 
water  and  open  the  bcrew  com- 
pressor a  little  at  a  time  under 
water.  As  soon  as  no  more  water 
will  run  in,  move  the  flask  so  that 
the  level  of  the  water  on  the  in- 
side is  the  same  as  that  on  the 
outside  (Fig.  24). 

Pinch  the  rubber  tube  with 
the  compressor  so  as  to  close  it, 
and  remove  the  flask  from  the 
water.  Set  it  in  a  secure  upright 
position  on  the  table.  Open  the 
compressor  so  as  to  allow  the  water 
in  the  small  tube  to  run  down  into  the  flask  and  then  re- 
move the  stopper  and  its  connections. 


Fig.  24. 


64  LABORATORY  EXERCISES 

Measure  with  a  graduate  the  volume  of  water  in  the 
flask. 

Record  the  measurements  in  tabular  form  near  the  top 
of  the  left-hand  page. 

OBSERVATIONS 

Weight  of  flask  filled  with  air g. 

Weight  of  flask,  air  exhausted g. 

Volume  of  air  exhausted cm.3 

Record,  if  so  directed  by  the  instructor,  the  temperature 
of  the  room  and  the  barometric  pressure. 

Briefly  describe  the  steps  in  the  experiment,  illustrat- 
ing with  drawings  from  your  apparatus. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 

Weight  of  air  exhausted g. 

Volume  of  air  exhausted cm.s 

Density  of  air grams 

cm* 
Discussion : 

After  the  water  had  run  into  the  flask,  the  water  levels 
were  made  the  same,  so  that  any  air  not  pumped  out  of 
the  flask  would  be  at  the  same  pressure  as  the  air  in  the 
room.  What  is  the  necessity  for  this  precaution  ?  Would 
the  results  obtained  for  this  experiment  be  exactly  the 
same  on  different  days  ?  Give  reasons  for  your  answer. 

Conclusion : 

The  density  of  the  air  in  the  laboratory  at  the  existing 
conditions  was grams  per  cubic  centimeter. 


DENSITY  OF  AIR  65 

EXPERIMENT   15    (Alternative) 

Density  of  Air 

OBJECT.  To  determine  the  approximate  density  of  air  in  the 
room. 

APPARATUS.  Incandescent  lamp  bulb;  Bunsen  burner  ;  blow- 
pipe ;  small  battery  jar ;  small  funnel  and  graduate ;  horn  pan 
balance  weighing  to  0.01  gram  or  better;  metric  weights;  small 
squares  of  adhesive  plaster.1 

Introductory : 

It  is  very  evident  that  lead  has  weight.  Even  a  small 
child  knows  that  a  tumbler  of  water  is  heavier  than  the 
empty  glass.  We  know  that  solids  and  liquids  have 
weight,  but  does  the  air  which  surrounds  us  have  weight  ? 
If  balloons  are  lighter  than  air,  then  air  must  have  weight. 
It  would  be  interesting  to  ascertain  just  how  dense  air  is, 
that  is,  the  number  of  grams  to  a  cubic  centimeter. 

Experimental : 

The  bulb  of  an  incandescent  lamp  is  empty  save  for 
the  filament  and  a  very  slight  trace  of  gas  which  was  not 
exhausted.  The  bulb  then  can  be  weighed  empty.  By 
making  a  small  hole,  t*he  air  will  rush  in  and  fill  the  bulb. 
Another  weighing  gives  the  weight  of  the  bulb  filled  with 
air.  The  difference  between  the  'two  weighings  is  the 
weight  of  the  air  in  the  bulb.  The  volume  of  this  air 
may  be  found  by  filling  the  bulb  with  water  and  then 
measuring  the  water  with  a  graduate.  With  the  weight 

1  Note  to  Instructor.  If  the  supply  of  burnt-out  bulbs  is  limited,  the 
experiment  may  be  done  in  small  squads,  each  student  making  the 
weighings  and  measurements  for  himself.  In  small  classes  the  instructor 
may  prefer  to  make  the  first  air  hole  with  the  blowpipe. 


66 


LABORATORY  EXERCISES 


Fig.  25. 


and  volume  of  the  air  known,  the  number  of  grains  per 

cubic  centimeter  can  be  calculated. 

Filling  the  Bulb  with  Air.  —  Use  the  tiny  point  of  a 

blowpipe  flame,  but  approach  the  portion  to  be  heated 
very  gradually  with  the  flame  so  as  to 
avoid  the  sudden  cracking  and  collapsing 
of  the  bulb.  Heat  a  small  area  near  the 
top  of  the  bulb  where  the  diameter  is 
greatest  (Fig.  25).  As  the  glass  softens 
at  the  tip  of  the  blowpipe  flame,  the  pres- 
sure of  the  outside  air  will  make  a  hole. 
Any  bits  of  glass  which  may  be  chipped 
off  will  tend  to  be  drawn  inward  «o  that 

there  will  be  no  loss  of  weight  due  to  the  glass.     Only  a 

tiny  hole  is  needed  to  admit  the  air. 

Filling  the  Bulb  with  Water.  —  After   the   bulb   has 

been  weighed  full  of  air,  heat  it  with  the  tip  of  a  blow- 
pipe flame  so  as  to  make  a  little  hole  in  the  glass  an  inch 

or  so  from  the  base  of  the  lamp. 

When  the  heated  glass  is  cool,  immerse  the  bulb  upright 

in  the  water  of  a  battery  jar  so  as  to  leave  the  first  air  hole 

made  just  above  the  surface  of  the  water 

(Fig.  26).    When  the  bulb  is  nearly  full, 

incline  the  bulb,  so  that  the  rest  of  the 

space  can  fill  with  water. 

Then  take  the  small  square  of  adhesive 

plaster   and  stick  over   the  lower  hole, 

holding  it  in   position  for  a   couple   of 

minutes  with  the  finger.     Now  cover  the 

upper  air  hole  with  the  finger  and  remove 

the  bulb  from  the  water.     Holding  the 

bulb  nearly  upright  over  a  funnel  sup- 
ported in  a  graduate,  pierce  through  the  adhesive  plaster 

just  over  the  lower  air  hole.     When  the  finger  over  the 


Fig.  26. 


DENSITY  OF  AIR  67 

upper  air  hole  is  removed,  the  water  will  run  down  into 
the  funnel.  Remember  that  the  outward  flow  may  be 
stopped  at  any  time  by  closing  the  upper  hole  with  the 
finger. 

Record  the  measurements  in  tabular  form  near  the  top 
of  the  left-hand  page. 

OBSERVATIONS 

Weight  of  incandescent  bulb  empty    .     .     .     ,  .         g. 

Weight  of  bulb  filled  with  air g. 

Volume  of  air  filling  bulb cm.z 

Record,  if  so  directed,  the  temperature  of  the  air  in  the 
room  and  the  barometric  pressure. 

Describe  briefly  the  steps  in  the  experiment  and  illus- 
trate with  drawings  from  your  apparatus. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 

Weight  of  air  filling  bulb 

Volume  of  air  filling  bulb      ..... 

Approximate  density  of  air  ..... 

Conclusion : 

The  approximate  density  of  air  in  room  at  existing  con- 
ditions was grams  per  cubic  centimeter. 


68  LABORATORY  EXERCISES 

EXPERIMENT   16 

Boyle's  Law 

OBJECT.  To  find  how  the  volume  of  a  gas  varies  with  the  pres- 
sure exerted  upon  it. 

APPARATUS.  Barometer  ;  Boyle's  Law  apparatus  as  furnished 
by  dealers  in  scientific  instruments.  The  two  forms  recommended 
are :  ( 1 )  the  apparatus  with  the  closed  tube  ending  in  glass  stop- 
cock, and  the  open  tube  connected  with  the  closed  tube  by  heavy- 
walled  tubing ;  (2)  the  apparatus  with  both  tubes  dipping  into  a 
mercury  reservoir,  the  closed  tube  sealed  at  the  upper  end,  and 
a  small  bicycle  pump  to  produce  pressure  in  reservoir,  so  as  to 
make  mercury  rise  in  the  two  tubes.1 

MATERIAL.     Mercury,  if  not  supplied  with  the  apparatus. 

Introductory : 

A  bicycle  pump  takes  in  air  and  makes  it  occupy  a  much 
smaller  space.  We  know  that  the  air  in  the  inflated  tube 
is  under  much  greater  pressure  than  before.  Oxygen  is 
sold  in  steel  cylinders  filled  under  pressure.  When  the 
valve  is  opened,  many  jars  of  oxygen  may  be  obtained  from 
one  tank  for  experiments  in  the  chemical  laboratory. 
The  total  volume  of  the  jars  filled  is  far  greater  than  that 
of  the  cylinder,  for  the  oxygen  is  under  much  less  pressure 
in  the  jars  than  in  the  steel  tank.  The  two  instances  of 

1  Note  to  Instructor.  The  directions  for  this  experiment  have  been 
written  so  that  either  of  the  two  forms  of  apparatus  may  be  used.  Both 
forms  are  on  hand  in  many  schools.  A  good  type  of  the  first  apparatus 
may  be  obtained  from  the  C.  H.  Stoelting  Co.,  Chicago  (list  number  1151) ; 
the  second  form  with  an  improved  mercury  reservoir  is  made  by  the 
L.  E.  Knott  Apparatus  Co.,  Boston  (list  number  41-105). 

The  authors  regard  the  J-tube  form  as  very  desirable  for  demonstration 
purposes,  but  less  fit  for  the  laboratory  experiment,  as  most  students  are 
unable  to  handle  it  without  spilling  the  mercury  required. 


BOYLE'S  LAW  69 

the  inflated  tire  and  the  filling  of  jars  with  oxygen  show 
that  there  is  some  relation  between  the  volume  of  the  gas 
and  the  pressure  exerted  on  it.  Whether  or  not  there 
is  any  regularity  in  this  relation,  may  be  ascertained 
by  experiment. 

Experimental : 

Specific  directions  for  handling  the  apparatus  will  be 
given  by  the  instructor. 

The  volume  of  air  used  is  that  inclosed  above  the 
mercury  in  the  closed  tube.  The  mercury  in  the  open 
tube  is  used  for  varying  the  pressure  upon  the  inclosed 
air.  When  the  mercury  levels  are  the  same  in  the  two 
tubes,  the  inclosed  air  is  under  atmospherio  pressure. 
When  the  mercury  level  is  higher  in  the  open  tube, 
then  the  inclosed  air  is  under  more  than  atmospheric 
pressure,  for  a  column  of  mercury  equal  in  height  to  the 
difference  in  levels  is  adding  its  pressure  to  the  atmospheric 
pressure.  A  lower  level  in  the  open  tube  means  a  pressure 
less  than  the  atmospheric. 

The  pressure  is  expressed  in  centimeters  of  mercury. 
If  the  bore  of  the  closed  tube  is  of  uniform  diameter,  the 
length  of  the  inclosed  air  column  may  be  taken  as  the 
measure  of  its  volume  and  recorded  in  centimeters. 

Make  a  number  of  readings,  as  directed  by  the  in- 
structor. The  difference  of  the  mercury  levels  in  the 
open  tube  between  successive  readings,  should  be  about 
10  cm.  One  reading  should  be  made  with  the  mercury  at 
the  same  level  in  the  two  tubes. 

As  soon  as  the  readings  are  made,  record  them  in  tabu- 
lar form  at  the  top  of  the  left-hand  page. 

Write  a  simple  description  of  the  method  of  using  the 
apparatus  and  make  an  outline  drawing  of  it,  showing  the 
essential  parts. 


70 


LABORATORY  EXERCISES 
OBSERVATIONS 


NUMBER  OP 
READING 

Oow 

MN  OF  INCLOSED  AIR 

MERCERY  LEVBL 
OPEN  TUBE 

Top 

Bottom 

1 

cm. 

cm. 

cm. 

2 

cm. 

cm. 

cm. 

etc. 

.  =        cm. 


Barometric  pressure  at  ---------  on  ---------  was  -----  mm.  = 

(.time)  (date) 

Place  the  calculated  results  in  tabular  form  at  the  top 
of  the  right-hand  page.  The  difference  in  the  mercury 
levels  can  be  found  from  the  quantities  in  the  last  two 
columns  of  the  table  of  observations. 

The  pressure  of  the  inclosed  air  is  atmospheric  pressure 
plus  or  minus  (as  the  case  may  be)  the  difference  of 
mercury  levels.  In  recording  the  product  of  the  pressure 
by  the  volume,  omit  the  decimal  fractions. 

CALCULATED  RESULTS 


NUMBER  OF 
READING 

DlFFEEENCE 

IN  LEVELS 

PRESSURE  OF 
INCLOSED  AIR 

VOLUME  OF 
INCLOSED  AIR 

PRESSURE  X 
VOLUME 

1 

cm. 

cm. 

cm.8 

2 

cm. 

cm. 

cm.8 

etc. 

Discussion : 

Is  the  product  of  the  pressure  and  the  volume  approxi- 
mately constant  ?  Why  should  the  temperature  of  the 
inclosed  air  not  change  while  the  readings  are  being  made? 
Would  a  variation  in  the  barometric  pressure  during  the 
experiment  affect  the  result  ? 

Conclusion : 

Complete  the  following  statement : 

At  a  constant  temperature,  the  volume  of  a  given  mass 
of  gas  varies as  the  pressure  sustained  by  it. 


MEASUREMENT  OF  GAS  PRESSURE  71 

EXPERIMENT   17 

Measurement  of  Gas  Pressure 

OBJECT.    To  measure  the  pressure  of  the  laboratory  gas  supply. 

APPARATUS.  Water  manometer,  consisting  of  a  U-tube  (8") 
with  one  arm  carrying  a  tightly  fitting  1-hole  rubber  stopper  with 
glass  elbow  tube ; l  block  with  slot  or  groove  for  supporting  U-tube  ; 
foot  rule  or  a  metric  scale ;  rubber  tubing  for  connecting  ma- 
nometer with  gas  cock  ;  barometer. 

Introductory : 

The  bag  of  a  balloon  connected  with  a  gas  main,  fills 
and  rounds  out  as  the  gas  rushes  in.  One  can  feel  the 
gas  pressing  out  when  a  stopcock  is  opened  from  the  gas 
supply  in  the  laboratory.  The  balloon  fills  and  the  gas 
rushes  into  the  room  despite  the  fact  that  the  weight  of 
the  air  is  pressing  around  the  bag  of  the  balloon  and 
against  the  opening  of  the  gas  cock.  This  pressure,  which 
is  effective  against  the  atmospheric  pressure,  may  be  de- 
scribed as  the  effective  pressure  of  the  gas  supply.  How 
much  is  the  effective  pressure  of  the  gas  delivered  to  our 
homes  and  school  ? 

Experimental : 

Enough  water  is  added  to  the  U-tube  to  fill  it  about 
halfway  up,  and  then  the  stopper  carrying  the  elbow  tube 
is  pressed  tightly  into  one  arm  of  the  tube.  The  water 
levels  in  the  two  arms  are  at  the  same  height,  since  the 
air  presses  down  on  both  water  surfaces  equally. 

The  elbow  tube  is  connected  by  a  rubber  tubing  with 

1  Instead  of  the  U-tube,  a  U-shaped  bend  of  glass  tubing  with  the  arras 
about  8  "  long,  may  be  used.  A  Skidmore  stand  is  very  convenient  for 
supporting  the  U-tube. 


72 


LABORATORY  EXERCISES 


the  gas  supply.  The  gas  stopcock  is  slowly  turned  on 
and  the  difference  in  the  height  of  the  water  levels  meas- 
ured. This  measurement  should  be  made  as  soon  as  the 
rising  water  level  reaches  its  greatest  height. 

OBSERVATIONS 

Atmospheric  pressure  (barometer  reading}  .     .  in. 

Difference  in  height  of  water  levels    ....  in. 

Time  when  readings  were  made 

If  the  measurements  were  made  in  centimeters,  change 

them  to  inches  by  multiplying  by  0.3937. 

Write  a  simple  description 
of  the  experiment  and  make 
a  drawing  showing  how  your 
apparatus  indicated  the  gas 
pressure. 

The  difference  of  the  water 
levels  due  to  the  increased 
pressure  is  independent  of  the 
cross  section  of  the  U-tube, 
therefore  we  can  consider  its 
cross  section  to  be  1  square 
inch.  A  pressure  of  14.7 
pounds  to  the  square  inch 
holds  up  a  water  column 
33.57  feet  in  length.  From 
this  equivalent,  calculate  the 
pressure  in  pounds  per  square 
inch  of  a  column  of  water 
equal  in  height  to  the  differ- 
ence of  levels  measured  in 

the  U-tube.     This  will  give  the  effective  pressure  of  the  gas. 
A  pressure  of  14.7  pounds  to  the  square  inch  holds  up 


Fig.  27. 


MEASUREMENT  OF  GAS  PRESSURE  73 

a  mercury  column  30  inches  in  length.  From  this  rela* 
tion,  calculate  the  pressure  in  pounds  per  square  inch 
which  is  equivalent  to  the  observed  barometric  reading. 

Adding  the  effective  pressure  to  the  atmospheric  pres- 
sure gives  the  total  pressure  of  the  gas,  that  is,  the  pressure 
per  square  inch  within  the  gas  pipes. 

Record  the  calculated  results  in  a  table  at  the  top  of 
the  right-hand  page. 

CALCULATED  RESULTS 

Effective  pressure  of  gas  per  sq.  in.    .     .     . 

Atmospheric  pressure  per  sq.  in 

Total  pressure  of  gas  per  sq.  in 

Discussion : 

Why  is  it  not  necessary  to  remove  the  air  in  the  arm 
of  the  U-tube  connected  with  the  gas  supply?     What  is 
the  gas  pressure  stated  to  be  in  your  town  or  city  ?    What 
does  this  mean  ? 
Conclusion : 

The  effective  pressure  of  the  gas  in  the  laboratory  at 
on was pound  per  square  inch.  The  total 

(time)  (date) 

pressure  per  square  inch  in  the  gas  pipes  was pounds. 


74  LABORATORY  EXERCISES 

EXPERIMENT   18 

Water  Pumps 

OBJECT.  To  study  the  parts  and  the  operation  of  the  simple 
lift  pump  and  the  force  pump. 

APPARATUS.     Glass  models  of  a  lift  pump  and  a  force  pump  ; 
3  feet  of  glass  tubing  (^")  with  a  short  piece  of  rubber  tubing 
'  attached ;  battery  jar. 

Introductory : 

The  ordinary  suction  or  lift  pump  has  been  used  for  over 
two  thousand  years.  Although  both  the  lift  pump  and 
the  force  pump  are  articles  of  familiar  appearance,  few 
can  give  an  intelligent  explanation  of  their  operation. 
In  these  cases,  as  in  other  apparently  simple  devices,  the 
study  of  the  principles  upon  which  they  are  based  proves 
fascinating. 

Experimental : 

CAUTION.  Handle  the  glass  models  with  great  care.  Do  not 
spill  water  around  the  laboratory. 

(a)  Place  in  a  jar  of  water  the  lower  end  of  a  long 
glass  tube  which  has  a  short  rubber  tube  on  the  upper 
end.  Compare  the  water  levels  in  the  tube  and  in  the 
jar.  Account  for  the  relative  levels. 

Suck  out  through  the  rubber  tube  most  of  the  air  in  the 
glass  tube,  noting  the  action  of  the  water.  Pinch  tightly 
the  upper  end  of  the  rubber  tube.  Does  the  water  run 
back  ?  What  pressure  holds  up  the  column  of  water  in  the 
glass  tube?  Release  the  pressure  on  the  rubber  tube. 
What  happens?  Explain.  Why  is  it  necessary  to  remove 
some  of  the  air  in  a  tube  if  we  want  water  to  be  pressed  up 
in  it  ? 


WATER  PUMPS 


75 


Make  three  simple  diagrams  which  will  show 
what  was  done  in  this  part  of  the  experiment 
and  indicate  the  results. 

(i)  The  Lift  Pump.  —  Examine  a  glass  model 
of  a  lift  pump,  noting  the  suction  tube,  the  bar- 
rel, the  piston,  the  two  valves,  and  the  spout. 
Make  an  outline  drawing,  labeling  the  parts. 
Starting  without  any  water  in  the  pump,  im- 
merse the  suction  tube  in  a  jar  of  water  and 
operate  the  pump  till  it  is  in  full  action,  noting 
the  action  of  the  inclosed  air,  the  water,  and  the 
two  valves  on  each  successive  stroke.  Record 
the  observations  in  tabular  form  on  the  left-hand 
page.  What  is  the  main  thing  accomplished  by 
the  first  few  strokes  of  the  pump  ? 


Fig.  28. 


OBSERVATIONS  ON  THE  LIFT  PUMP 


STROKE 

VALVE 

ACTION  OP  AIE 

ACTION  OF  WATER 

ACTION  AND 
USE  OK  VALVK 

1st  Up 

Lower 

1st  Up 

Upper 

1st  Down 

Lower 

1st  Down 

Upper 

2dUp 

Lower 

2dUp 

Upper 

etc. 

etc. 

(c)  By  a  rubber  connection  attach  a  long  glass  tube 
to  the  suction  pipe  of  the  lift  pump.  Dip  the  free  end  of 
the  long  tube  into  a  jar  of  water  placed  on  the  laboratory 
floor.  Can  you  pump  water  from  the  floor?  What  limits 
the  vertical  distance  through  which  water  can  be  taken  by  a 
lift  pump  even  though  it  were  mechanically  perfect  ? 


76 


LABORATORY  EXERCISES 


(i?)  The  Force  Pump.  —  Examine  the  glass  model  of  a 
force  pump,  noting  its  parts.  Try  its  action. 

Make  two  diagrams  showing  the  action 
of  the  pump  —  one  for  the  up  stroke,  the 
other  for  the  down.  Show  water  levels, 
and  use  arrows  to  indicate  the  direction 
of  water  flow. 

Will  the  force  pump  or  the  lift  pump 
raise  water  to  a  higher  level  ?  Why  is 
this  so? 

Do  not  write  a  description  of  the  work 
done,  as  the  drawings  and  tabulations 
show  this.  A  few  explanatory  statements 
may  be  added  if  necessary. 

Discussion : 

Under  this  heading,  on  the  right-hand 


Fig.  29. 


page,  answer  the  italicized  questions  in  the 
experimental  directions. 
Is  the  action  of  these  pumps  due  to  pressure  or  to  "  suc- 
tion."    Which  type  of  pump  is  a  bicycle  pump  ?     Explain. 
Why  is  a  little  water  sometimes  poured  in  at  the  top 
of  a  pump  just  before  working  the  handle?     (Class  Dis- 
cussion.) 


THE  PRINCIPLE  OF  MOMENTS  77 

EXPERIMENT   19 

The  Principle  of  Moments 

OBJECT.  When  three  parallel  forces  are  in  equilibrium,  to  com- 
pare (a)  the  forces  in  one  direction  with  the  force  in  the  opposite 
direction;  (&)  the  clockwise  moments  with  the  counterclockwise 
moments. 

APPARATUS.  Meter  stick ;  loops  of  strong  cord ;  3  spring  balances 
(2000  grams),  with  hooks  for  suspending  them,  or  clamps  for 
fastening  the  balances  to  the  edge  of  the  table  top  (Fig.  35).1 

Introductory : 

When  a  team  of  horses  is  drawing  a  wagon,  their  com- 
bined force  forward  is  exerted  to  overcome  the  resistance 
of  the  wagon  pulling  backward.  When  two  boys  carry  a 
heavy  weight  suspended  from  a  stick,  the  boys  pull  up- 
ward and  the  weight  pulls  downward.  If  the  boys  have 
not  equal  strength,  the  weight  will  be  shifted  toward  one 
of  the  boys.  Which  one? 

In  each  of  these  cases,  we  have  three  forces  parallel  to 
each  other,  two  in  one  direction  and  one  in  the  opposite. 
These  forces  are  in  equilibrium  when  the  stick  is  balanced. 
If  one  boy  should  lift  more  than  he  had  been  lifting,  the 
stick  would  turn  toward  him.  The  turning  effect  of  a 
force  is  called  the  moment  of  the  force. 

We  can  imitate  either  of  these  cases  by  attaching  three 
spring  balances  to  a  meter  stick,  so  that  two  pull  in  one 
direction  and  one  in  the  other.  We  can  then  compare 
(a)  the  pull  of  the  two  forces  in  one  direction  with  that 

1  This  experiment  can  also  be  conveniently  done  by  using  two  balances 
suspended  vertically  with  a  weight  between,  supported  by  a  loop  on  the 
meter  stick  so  that  the  weight  may  be  moved  to  positions  of  equilibrium. 
If  this  modification  is  made,  allowances  must  be  made  for  the  pull  on  the 
balances  due  to  the  weight  of  the  meter  stick. 


78  LABORATORY  EXERCISES 

of  the  single  force  in  the  other,  and  compare  (6)  the  turn- 
ing effect  or  moment  of  the  force  at  one  end  with  that 
of  the  force  at  the  other  end  of  the  stick. 

Experimental : 

The  apparatus  will  be  arranged  as  shown  in  the  diagram 
(Fig.  30).  The  amount  of  each  force  may  be  read  on  the 
balance.  First  each  outside  cord  should  be  placed  10  cm. 

from  its  end  of  the  meter 
~  stick  and  the  third  cord 
in  the  center.     See  that 
all    cords    are    parallel. 
The  highest   reading  on 
]    any  balance   should   not 
be  more  than  1600  grams. 
When  all  is  adjusted,  the 
reading  of   each  balance 
and  the  position  of  each 
Fig.  30.  string  on  the  meter  stick 

should  be  recorded  (I). 

One  end  balance  may  then  be  shifted  so  that  it  is  half 
as  far  from  the  center  as  the  other.  After  adjustment, 
readings  should  again  be  taken  (II).  The  total  force  in 
one  direction  may  then  be  compared  with  the  total  force 
in  the  other,  as  indicated  in  the  table  for  the  right-hand 
page.  The  moment  of  a  force  is  found  by  multiplying 
the  force  by  its  lever  arm.  The  lever  arm  is  the  perpen- 
dicular distance  from  the  fulcrum  a-bout  which  the  force  is 
trying  to  turn  the  body,  to  the  force.  In  this  experiment, 
the  distance  between  each  of  the  outer  cords  and  the  center 
cord  will  be  the  lever  arm  for  the  force  ipplied  by  the 
cord,  if  the  cords  are  at  right  angles  to  the  meter  stick. 
The  moment  of  each  of  the  end  forces  around  the  center 
cord  is  to  be  computed. 


THE  PRINCIPLE  OF  MOMENTS  79 

Record  the  readings  in  tabular  form  near  the  top  of  the 
left-hand  page. 

OBSERVATIONS 

i  ii 

Reading  of  balance  A 

Reading  of  balance  B 

Reading  of  balance  C 

Point  of  application  of  force  A  . 
Point  of  application  of  force  B  . 
Point  of  application  of  force  0 . 

Make  a  drawing  of  your  apparatus  and  write  a  simple 
description  of  how  it  was  used.  Place  the  table  of  calcu- 
lated results  at  the  top  of  the  right-hand  page. 

CALCULATED  RESULTS 

i             ii 
Combined  Force  of  A  and  B      .     .     .     

Force  of  O 

Moment  of  A  ab out  C 

Moment  of  B  about  O 

Discussion : 

Is  the  moment  of  A  about  C  clockwise  or  counter- 
clockwise ?  Is  the  moment  of  B  about  0  clockwise  or 
counterclockwise  ? 

Conclusion : 

Complete  the  following  with  a  statement  about  the 
amount  of  force  in  each  direction  : 

When  three  parallel  forces  act  on  the  same  body  to  pro- 
duce equilibrium,  then 

Complete  the  following  by  comparing  with  the  moment 
of  the  third  force  around  the  second,  both  as  to  magnitude 
and  direction : 

When  three  parallel  forces  act  on  the  same  body  to 
produce  equilibrium,  the  moment  of  one  of  them  about 
the  second  is___ 


80 


LABORATORY  EXERCISES 


EXPERIMENT    20 

The  Lever  Arm  of  a  Force 

OBJECT.    To  determine  the  lever  arms  of  non-parallel  forces. 

APPARATUS.  Meter  stick,  with  a  hole  on  the  center  division 
near  one  edge,  drilled  slightly  larger  than  the  shank  of  a  f  "  screw 
eye;  short  piece  of  board  about  f"  stock ;  screw  eye,  £" ;  fish 
line;  four  clamps;  half  meter  stick;  draughtsman's  triangle, 
90°,  60°,  and  30.° 

Introductory : 

In  using  such  a  lever  as  a  crowbar,  pump  handle,  or 
hammer,  it  is  seldom  that  the  forces  exerted  on  and  by  the 
lever  are  parallel  to  one  another.  Under  such  circum- 
stances, it  would  be  desirable  to  know  whether  the  lever 
arm  is  to  be  measured  along  the  lever  or  at  right  angles  to 
the  applied  force. 


f&-^ 


Fig.  31. 


THE  LEVER  ARM  OF  A  FORCE        81 

Experimental : 

The  meter  stick  is  to  be  attached  by  the  screw  eye  to  a 
short  board  held  firmly  by  two  clamps  to  the  edge  of  the 
laboratory  table.  The 
meter  stick  must  be  free 
to  rotate  around  the  shank 
of  the  screw  eye  as  a  ful- 
crum. 

The  hook  of  each  bal- 
ance is  to  be  attached  by  a 
loop  to  the  meter  stick. 
The  other  end  of  each  bal- 
ance is  to  be  clamped  to 
the  edge  of  the  table  op- 
posite the  meter  siick.  These  two  balances  are  to  be 
clamped  so  that  they  make  acute  angles  with  the  meter 
stick.  One  angle  should  be  nearly  a  right  angle  and  the 
other  decidedly  acute,  as  shown  in  Fig.  31. 

Perpendicular  distances  may  be  measured  by  using  a 
triangle  and  a  half  meter  stick,  as  shown  in  Fig.  32. 

Make  the  following  readings  and  record  in  tabular  form 
near  the  top  of  the  left-hand  page  of  note-book. 

OBSERVATIONS 

Reading  of  balance  A g. 

Reading  of  balance  B g. 

Point  of  application  of  force  A    .....  cm. 

Point  of  application  of  force  B cm. 

Position  of  fulcrum  on  meter  stick    .     .     .     .  cm. 

Perpendicular  distance,  fulcrum  to  force  A     .  cm. 

Perpendicular  distance,  fulcrum  to  force  JB     .  cm. 

Make  one  drawing  showing  the  arrangement  of  your 
apparatus  and  another  drawing  showing  the  method  of 


82  LABORATORY  EXERCISES 

measuring  the  perpendicular  distance  of  a  force  from  the 
fulcrum.  Write  a  simple  description  of  Jiow  the  experi- 
ment was  done,  referring  to  the  drawings.  Place  the  table 
of  calculated  results  at  the  top  of  the  right-hand  page  and 
make  all  the  calculations  on  that  page. 

CALCULATED  RESULTS 

Distance  along  stick  from  fulcrum  to  a  .     .     .  cm. 

Distance  along  stick  from  fulcrum  to  b  .     .     .  cm. 

Force  A  x  meter  stick  distance  from  fulcrum  . 
Force  B  x  meter  stick  distance  from  fulcrum  . 
Force  A.  x  perpendicular  distance  from  fulcrum 
Force  B  x  perpendicular  distance  from  fulcrum 

Discussion : 

Which  pair  of  products,  in  the  table  above,  more  nearly 
agrees  with  the  principle  of  moments  ? 

Conclusion: 

How  should  the  lever  arm  of  a  force  always  be  measured? 


EXPERIMENT   21 

Composition  of  Several  Parallel  Forces 

OBJECT.  When  a  number  of  parallel  forces  are  in  equilibrium, 
to  compare  (a)  the  total  force  in  one  direction  with  the  total  force 
in  the  opposite  direction;  (6)  the  clockwise  moments  with  the 
counter-clockwise  moments. 

APPARATUS.  Meter  stick ;  four  or  more  spring  balances 
(2000  g.),  with  cords  and  clamps. 


COMPOSITION  OF  SEVERAL  PARALLEL  FORCES    83 


Introductory : 

A  floor  or  bridge  beam  is  frequently  supported  at  more 
than  two  points  and  has  a  number  of  different  persons  or 
objects  exerting  their  weights  on  it  at  various  points.  It 
is  interesting  to  determine  whether  the  principle  of 
moments  which  has  been  tested  for  two  forces  acting 
about  the  point  of  application  of  a  third  as  a  fulcrum, 
will  apply  to  this  case  also. 

Experimental : 

Four  or  more  spring  balances,  as  the  instructor  may 
direct,  are  to  be  attached  by  cords  to  a  meter  stick,  as  in 


1000  g 


TOO  g 


^750(7 


Scale  1cm =500  (7 


1800  fj 
Fig.  33. 

the  experiment  on  the  Principle  of  Moments  (see  Fig.  30, 
page  78).  The  balances  should  then  be  strained  and 
clamped  in  place  in  such  a  way  as  to  make  all  the  cords 
parallel,  and  at  right  angles  to  the  meter  stick. 

The  amounts  of  various  forces  and  their  lever  arms  are 
to  be  recorded  near  the  top  of  the  left-hand  page  in  the 
form  of  a  diagram  like  that  shown  in  Fig.  33.  Letter 
the  forces  in  order  from  left  to  right. 


84  LABORATORY  EXERCISES 

Take  for  the  center  of  moments  some  point  which  is 
not  the  point  of  application  of  any  of  the  forces.  The 
line  representing  each  force  should  be  drawn  to  a  scale  to 
be  designated  by  the  instructor  and  the  exact  amount  of 
the  force  should  be  noted  at  the  right  of  the  line  repre- 
senting it.  The  lever  arms  are  indicated  by  dimension 
lines  as  shown.  No  drawing  of  the  apparatus  will  be 
necessary.  A  short  description,  however,  of  the  experi- 
mental method  should  be  written. 

Place  a  table  like  the  following  at  the  top  of  the  right- 
hand  page  and  make  all  calculations  on  that  page: 

CALCULATED  RESULTS 


CLOCKWISE  MOMENTS 


COUNTERCLOCKWISE  MOMENTS 


Moment  of  A 


etc. 


Total  clockwise  moments    . 

Sum  of  forces  as  A,  C,  E,  etc. 
Sum  of  forces  as  B,  D,  etc. 


Moment  of  B  .     .     .     . 

etc 

Total   counterclockwise 


moments 


Conclusion : 

Fill  in  the  blanks  in  the  following  statement  so  that  it 
agrees  with  your  results: 

When  a  number  of  parallel  forces  act  on  a  body,  it  is 

in  equilibrium  when  the of  the  forces  in  one  direction 

equals  the of  the  forces  in  the  other  direction,  and 

the  total moments  equal  the  total moments 

about  any  point  taken  as  fulcrum. 


FOUR  FORCES  AT  RIGHT  ANGLES  85 

EXPERIMENT    22 

Four  Forces  at  Right  Angles 

OBJECT.  When  four  forces  at  right  angles  in  one  plane  produce 
equilibrium,  to  compare  (a)  the  force  in  any  one  direction  with  the 
force  in  the  opposite  direction ;  (&)  the  clockwise  moments  with  the 
counterclockwise  moments. 

APPARATUS.  Composition-of-force  board  with  under  side  rest- 
ing on  four  steel  balls  or  marbles ;  four  pegs  ;  four  spring  balances 
(2000  g.)  with  cords  and  clamps ;  meter  stick  or  other  metric  ruler. 

Introductory : 

Four  boys  of  different  ages  might  pull  on  the  four  sides 
of  a  piece  of  burlap  so  as  to  stretch  it  parallel  to  the  top 
of  a  barrel  of  vegetables  while  their  father  finished  the 
heading  by  putting  on  a  hoop.  Each  boy  probably  took 
hold  of  the  burlap  at  the  center  of  his  side,  but  one  or 
more  of  them  soon  found  it  advisable  to  move  his  hands 
to  one  side  or  the  other  of  the  center,  so  as  to  prevent  the 
burlap  from  being  drawn  out  of  his  hands.  When  the 
burlap  was  properly  stretched,  four  pulls  or  forces  were 
acting  at  right  angles  in  one  plane.  Did  the  principle  of 
moments  come  to  the  aid  of  the  smaller  boys  in  the 
family  so  that  they  could  do  their  share  of  the  stretching? 

Experimental : 

The  hook  of  each  spring  balance  is  to  be  attached  by  a 
cord  to  a  peg  on  the  composition-of-force  board.  The 
pegs  should  be  arranged  so  that  no  two  of  them  will  be  in 
the  same  row  of  holes  across  the  board  in  either  direction. 
The  other  end  of  each  spring  balance  is  to  be  securely 
clamped  (see  Fig.  35  on  page  89)  so  that  both  the  cords 
holding  it  are  parallel  to  a  row  of  holes  (Fig.  34).  This 


LABORATORY  EXERCISES 


latter  figure  shows  the  method  of  attachment  of  the  bal« 
ances  to  the  board,  but  not  the  correct  location  of  the  pegs. 
The  strain  on  each  balance  should  be  at  least  500  grams, 

and  the  board,  which  is 
free  to  move  on  its  roller 
bearings,  should  be 
brought  to  rest  by  the 
equilibrium  of  the  four 
forces  at  right  angles 
pulling  on  it. 

The  amounts  of  the  va- 
rious forces  and  their 
lever  arms  are  to  be  re- 
corded in  the  form  of  a 
diagram  on  the  left-hand 
page.  Draw,  in  about 
the  middle  of  this  page,  a  square,  7  centimeters  on  a  side, 
and  divide  each  side  into  centimeter  divisions,  and  lightly 
rule  such  cross  lines  as  will  locate  the  positions  of  the  four 
pegs  or  points  of  application  of  the  several  forces. 

Take  for  the  center  of  moments  some  point  which  is 
not  the  point  of  application  of  any  of  the  forces.  To  a  scale 
designated  by  the  instructor,  draw  a  line  representing  the 
direction  and  the  exact  amount  of  each  force.  Indicate 
the  amount  of  each  force  by  figures  placed  to  the  right  of 
the  line  representing  it.  The  lever  arm  of  each  force  is  to 
be  indicated  by  a  dimension  line  as  in  Fig.  33,  on  page  83. 

CALCULATED  RESULTS 


Fig.  34. 


CLOCKWISE  MOMENTS 

COUNTERCLOCKWISE  MOMENTS 

Moment  of  

Moment  of      

etc                     .... 

Total  clockwise  moments  . 

Total  counterclockwise 
moments   . 

~ 

PARALLELOGRAM  OF  FORCES  87 

Unless  the  instructor  so  directs,  make  no  drawing  of 
the  apparatus.  A  short  description  of  the  experimental 
method,  however,  should  be  written. 

Place  a  table,  like  the  one  on  page  86,  at  the  top  of  the 
right-hand  page  and  make  all  calculations  on  that  page. 

Conclusion : 

State,  when  four  forces  at  right  angles  in  one  plane  pro- 
duce equilibrium : 

(a)  the  relation  of  the  force  in  one  direction  to  the  force 
in  the  opposite*  direction ; 

(6)  relation  of  the  clockwise  moments  to  the  counter- 
clockwise moments  about  any  point  taken  as  a 
fulcrum. 

EXPERIMENT    23 

Parallelogram  of  Forces 

OBJECT.  To  find  the  relation  between  three  forces  acting  on  a 
body  at  a  point,  in  order  that  they  may  be  in  equilibrium. 

APPARATUS.  3  spring  balances  (2000  g.)  ;  fish  line  or  other 
light,  strong  cord ;  3  Stone  clamps  or  other  means  of  hold- 
ing balances  in  place  ;  30  cm.  ruler. 

Note.  —  Pencils  used  in  this  exercise  should  be  hard,  with  long, 
sharp  points. 

Introductory : 

If  two  boys  were  to  kick  a  football,  one  east  and  the 
other  north,  at  the  same  instant,  the  ball  would  not  go  in 
either  direction,  but  would  take .  a  course  somewhere  .be- 
tween north  and  east.  The  general  direction  that  it  would 
take  would  depend  upon  which  force  were  greater.  To 
prevent  the  football  from  moving,  it  would  be  necessary 


88  LABORATORY  EXERCISES 

to  apply  a  third  force  which  should  have  the  proper  direc- 
tion and  amount  to  just  neutralize  the  other  two.  We 
wish  to  find  the  relation  between  three  forces  at  an  angle 
to  each  other,  acting  on  a  body  at  a  point  in  such  a  way 
as  to  keep  the  body  at  rest.  With  the  football  it  would 
be  possible  for  a  single  force  to  be  substituted  for  the 
forces  applied  by  the  two  boys.  Such  an  imaginary  force 
is  known  as  a  resultant  force,  and  the  two  forces  which  it 
replaces  are  component  forces.  The  single  force  that 
would  keep  the  ball  from  moving  is  called  the  equilibrant 
force.  Our  problem  is  to  find  (a^  how  the  resultant  force 
is  related  to  the  component  forces  in  direction  and  magni- 
tude ;  (5)  how  the  resultant  force  is  related  to  the  equili- 
brant force. 

Experimental : 

Connect  the  three  spring  balances  by  three  cords  that 
meet  at  a  point  A.  Fasten  these  balances  in  place 
by  clamping  the  attached  wires.  Pull  on  the  third  balance 
until  the  pointer  on  one  of  the  balances  is  near  the  end  of 
the  scale  and  then  clamp  the  third  balance  in  place. 

Place  the  right-hand  page  of  the  note-book  under  the 
cords  with  the  center  of  the  page  under  the  point  A. 
Mark  two  points  directly  beneath  each  cord.  Remove  the 
book  and  through  each  pair  of  points  draw  a  line  which 
represents  in  direction  the  force.  Note  and  record  on  the 
diagram,  the  reading  of  each  balance,  calling  the  balances 
B,  C,  and  D.  Measure  from  A  along  each  line  a  distance 
to  represent  the  magnitude  of  the  force,  using  a  scale  of 
1  cm.  to  250  grams.  Place  at  the  end  of  each  line  an 
arrowhead  to  show  the  direction  of  the  force. 

Select  one  force  as  the  equilibrant  and  lay  off  from  A 
the  resultant  equal  and  opposite  to  the  equilibrant.  On 
the  two  lines  representing  the  components,  erect  a  parallel- 


PARALLELOGRAM  OF  FORCES  89 

ogram  and  draw  the  diagonal  from  A.  Determine  the 
magnitude  of  the  force  which  this  diagonal  would  repre- 
sent. Compare  it  with  the  resultant  which  you  laid  off 
and  drew. 

Mark  on  the  drawing  the  lengths  of  the  lines  and  the 
readings  of  the  balances.     No  table  of  results  is  necessary 


Fig.  35. 

on  the  left-hand  page,  but  write  a  simple  description  of 
the  method  of  the  experiment.  The  drawing  has  already 
been  placed  on  the  right-hand  page. 

On  the  second  right-hand  page  place  the  table  of  calcu- 
lated results. 

CALCULATED  RESULTS 


Magnitude  of  resultant g. 

Magnitude  represented  by  diagonal     ....          g. 

Discussion: 

(1)  What  single  force  would  alone  produce  the  same 
effect  as  the  two  forces  represented  by  the  sides  of  the 


90  LABORATORY  EXERCISES 

parallelogram?     (2)  Compare  the  resultant  and  the  diag- 
onal of  the  parallelogram  in  direction  and  in  magnitude. 

Conclusion : 

Three  forces  are  in  equilibrium  when  the of  two  of 

them  is in  magnitude  and in  direction  to  the . 


EXPERIMENT  24 

Resolution  of  Forces 

OBJECT.  Given  the  resultant  of  two  forces  and  one  of  the  forces, 
to  find  the  other  force. 

APPARATUS.  2  spring  balances  (2000  g.)  ;  500-gram  weight ; 
fish  line ;  upright,  with  ring  for  cord  and  notch  for  boom  ;  light 
hard-wood  boom,  about  25  cm.  long,  with  a  brad  in  the  end. 

Introductory : 

When  a  load  is  hanging  from  the  boom  of  a  derrick,  its 
weight  is  sustained  jointly  by  the  tension  of  the  rope  sup- 
porting the  end  of  the  boom  and  the  outward  thrust  of 
the  boom.  These  two  forces  may  then  be  considered  as 
the  component  forces,  whose  resultant  balances  the  weight 
of  the  load.  If  we  know  the  pull  on  the  cord  supporting 
the  boom  and  the  weight  of  the  load,  we  can  calculate 
the  thrust  of  the  boom  outward. 

Experimental : 

(a)  The  apparatus  is  to  be  set  up  as  shown  in  Fig.  36. 
The  boom  should  be  horizontal,  and  when  it  has  been  made  so, 
a  turn  of  the  cord  around  the  brad  in  the  end  of  the  boom 
will  keep  it  from  slipping.  When  all  adjustments  have 


RESOLUTION  OF  FORCES 


91 


Fig.  36. 


been  made,  hold  the  note-book  with  the  right-hand  page 
against  the  boom,  and  indicate  the  direction  of  the  forces 
by  dots  under  the 
cords  and  a  line 
drawn  along  the 
top  of  the  boom. 
Place  a  dot  at  the 
end  of  the  boom, 
immediately  under 
the  brad.  Leave  the 
apparatus  undis- 
turbed while  per- 
forming the  oper- 
ations of  part  (6). 

(J)  Replace  the 

note-book  on  the  table.  From  the  dot  marking  the  com- 
mon point  of  application  of  the  forces,  draw  lines  through 
the  dots  that  were  placed  under  the  cords.  From  the 
common  point  of  application,  continue  outward  some  dis- 
tance the  line  drawn  along  the  boom.  Lay  off  on  the 
line  representing  the  tension,  a  distance  corresponding  to 
the  reading  of  the  balance,  using  a  scale  of  100  grams  to 
the  centimeter.  Mark  the  end  of  the  measured  distance 
with  an  arrowhead,  indicating  the  direction  of  the  force. 
Do  the  same  on  the  line  representing  the  weight.  Mark 
beside  each  line  the  exact  number  of  grams  represented. 

The  weight  is  the  equilibrant  of  the  tension  of  the 
cord  and  the  outward  push  or  thrust  of  the  boom  against 
the  cord.  Therefore  draw  a  line  upward  from  the  point 
of  application  equal  in  length  to  the  line  representing  the 
weight.  With  this  line  as  a  diagonal  and  the  line  repre- 
senting the  tension  as  one  side,  complete  a  parallelogram 
having  a  side  extending  outward  from  the  point  of  applica- 
tion, as  a  continuation  of  the  line  drawn  along  the  boom. 


92  LABORATORY  EXERCISES 

This  side  will  represent  the  thrust  in  direction  and  magni- 
tude. From  the  length  of  this  side,  the  outward  thrust 
of  the  boom  may  be  calculated,  using  the  scale  employed 
in  laying  off  the  other  lines. 

(c)  Hook  a  second  spring  balance  between  the  cord 
and  the  boom  and  pull  horizontally  until  the  boom  just 
slips  out  of  the  notch  in  the  upright.  Read  the  balance 
at  this  point  and  record  below  the  drawing  on  the  right- 
hand  page  : 

Force  required  to  pull  out  boom   ....  g. 

Since  action  and  reaction  are  equal,  the  inward  compo- 
nent of  the  stretched  cord  on  the  boom  must  equal  the  out- 
ward thrust  of  the  boom  on  the  cord. 

Make  a  simple  sketch  of  your  apparatus  and  write  a 
brief  description  referring  to  the  sketch. 

Discussion : 

May  the  resultant  of  two  forces  ever  be  less  than  one  of 
them? 

Is  a  rope  that  is  just  strong  enough  to  lift  a  weight 
vertically,  strong  enough  to  lift  that  weight  by  means  of  a 
horizontal  boom  derrick  ? 

Conclusion : 

Given  the  resultant  of  two  component  forces  and  one  of 
the  components,  state  how  the  other  component  may  be 
found. 


FORCE  AT  THE  CENTER  OF  GRAVITY  93 

EXPERIMENT   25 

Force  at  the  Center  of  Gravity  of  a  Body 

OBJECT.  To  find  what  is  the  gravitational  force  acting  at  the 
center  of  gravity  of  a  body. 

APPARATUS.  Half  meter  stick  loaded  at  one  end;1  ruler  or 
other  fulcrum  properly  supported  (see  Fig.  37)  ;  200-gram  weight 
with  loop  of  cord  attached;  spring  balance,  or  platform  balance  ; 
metric  weights. 

Introductory : 

When  we  shut  a  heavy  door,  we  push  near  the  outside 
of  the  door  and  not  near  the  hinge.  A  small  rjoy  can 
balance  a  large  boy  on  a  seesaw,  loy  sitting  farther  out 
on  the  board.  When  a  body  is  to  be  turned  about  an 
axis,  the  turning  power  depends  upon  how  much  force  is 
exerted  and  how  far  from  the  axis  the  force  is  exerted. 
The  turning  power  of  a  force  is  called  the  moment  of  that 
force  and  is  measured  by  the  product  of  the  force  and  its 
distance  from  the  axis.  The  moment  of  the  small  boy  on 
the  seesaw  is  equal  to  the  moment  of  the  large  boy.  If 
we  know  the  moment  of  the  large  boy  and  the  distance 
of  the  small  boy  from  the  fulcrum,  we  can  calculate  what 
the  small  boy  weighs.  If  both  boys  get  off,  the  board 
can  be  balanced  so  it  will  not  touch  at  either  end.  The 
point  at  which  a  body  must  be  balanced  in  order  to  sup- 
port it  is  called  the  center  of  gravity  of  the  body. 

Experimental : 

The  body  will  be  a  half  meter  stick  loaded  at  one  end. 
This  is  first  to  be  balanced  over  a  fulcrum  in  order  to  find 

1The  loading  may  be  done  by  attaching  a  strip  of  brass,  iron,  01 
lead  to  one  end  of  the  half  meter  stick,  at  right  angles  to  the  stick. 


94 


LABORATORY  EXERCISES 


the  center  of  gravity  (Fig.  37,  A*).  Then  a  200-gram 
weight  will  be  hung  about  10  cm.  from  the  free  end  of  the 
bar  and  the  bar  again  balanced. 

By  measuring  the  distance  of  the  200-gram  weight  from 
the  fulcrum  and  multiplying  this  distance  by  the  weight 
(200  g.),  the  moment  of  the  200-gram  weight  is  obtained. 


Fig.  37. 

This  moment  equals  the  moment  of  the  force  at  the  center 
of  gravity  about  the  fulcrum.  Then  the  force  at  the 
center  of  gravity  is  calculated. 

A  second  trial  should  be  made  with  the  weight  at  some 
other  point  on  the  stick,  as  20  cm.  from  the  end. 

Finally  the  loaded  stick  is  weighed. 

All  observations  as  soon  as  made  should  be  recorded  in 
tabular  form  near  the  top  of  the  left-hand  page. 

OBSERVATIONS 

Position  of  center  of  gravity  of  loaded         i  2 

stick 

Position  of  2QQ-g.  weight 

Position  of  fulcrum  for  equilibrium      .  

Weight  of  loaded  stick 


FORCE  AT  THE  CENTER  OF  GRAVITY  95 

Make  drawings  showing  how  your  apparatus  was  used 
and  write  a  simple  description  of  how  the  experiment  was 
done. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 

i              a 
Distance  of weight  from  fulcrum  (Z)x)        

Distance   of    center   of  gravity  from 
fulcrum  (J92)      .....'.  

Moment     of     weight     about   fulcrum 

(200  xDj) 

Moment  of  force  at  center  of  gravity 

Calculated  force  at  center  of  gravity  

Discussion : 

Define  moment  of  force.  Explain  the  calculation  of  the 
moment  of  the  force  at  the  center  of  gravity  and  the  cal- 
culation of  the  amount  of  this  force. 

Conclusion : 

What  gravitational  force  acts  at  the  center  of  gravity  of 
a  body.  (Compare  the  last  item  in  both  tables.) 


96  LABORATORY  EXERCISES 

EXPERIMENT   26 

The  Pendulum 

OBJECT.  To  observe  the  effect  on  the  number  of  vibrations  of 
a  pendulum  in  one  minute  of  (a)  change  in  mass,  (&)  change  in 
amplitude,  (c)  change  in  length. 

APPARATUS.  A  wood  and  a  metal  ball  each  about  1  inch  in 
diameter  and  having  a  light  cord  about  125  cm.  long  attached; 
a  support  consisting  of  a  split  cork  in  a  burette  clamp,  or  a  special 
pendulum  clamp,  so  placed  that  the  pendulum  may  swing  freely 
in  front  of  the  laboratory  table ;  metronome  or  laboratory  clock 
with  telegraph  sounder. 

Note.  —  Some  instructors  prefer  to  have  all  pendulums  in  the 
room  released  at  a  given  signal  and  stopped  on  signal  at  the  end  of 
the  minute,  as  confusion  is  thereby  lessened  and  the  student's  mind 
is  concentrated  on  the  counting. 

Introductory : 

When  a  clock  goes  too  fast,  should  the  pendulum  be 
shortened  or  lengthened  ?  We  see  pendulums  made  of 
different  materials.  Does  this  affect  the  length  of  their 
beats  ?  Does  it  take  a  pendulum  longer  to  swing  through 
a  long  arc  than  a  small  one  ?  These  are  some  of  the  ques- 
tions the  experiment  will  help  to  answer.  By  a  vibration 
of  a  pendulum  is  meant  a  swing  from  one  end  of  its  arc 
to  the  other.  The  period  of  the  pendulum  is  the  time 
that  one  vibration  takes.  A  seconds  pendulum  is  one  that 
swings  from  one  end  of  the  arc  to  the  other  in  just  one 
second ;  a  half  seconds  pendulum  makes  one  vibration  in 
one  half  second  ;  etc.  The  frequency  of  the  pendulum  is 
the  number  of  vibrations  per  minute. 

Experimental : 

There  will  be  furnished  a  metal  and  a  wooden  ball 
of  the  same  size,  attached  to  a  light  cord  over  a  meter 


THE  PENDULUM 


97 


long.  As  the  suspending  cord  is  very  light,  we  neglect 
its  weight  and  consider  the  length  of  the  pendulum  as 
the  distance  from  the  lower  edge  of  the  support  to  the 
center  of  the  suspended  ball  or  "bob." 

For  the  first  test,  adjust 
the  length  of  the  pendulum 
with  the  wooden  ball  to  100 
cm.  Count  and  record  the 
number  of  vibrations  made  /  \ 

in    one     minute     swinging  / 

through  a  small  arc.     Re-  > 

place  with  the  metal  pen-  / 

duluni  and  find  how  many  / 

vibrations  that  makes  in  one 
minute    swinging    through    |  , 

the  same  arc.     Comparing 
these    numbers    will    show  / 

whether  or  not  the  material  / 

of  the  pendulum  affects  the  / 

period  of  vibration. 

Now  swing  the  metal  bob  Fig.  38. 

through    an    arc    twice    as 

great  as  before,  counting  the  number  of  vibrations  per 
minute.  Make  the  length  of  the  pendulum  50  cm.  and 
find  the  number  of  vibrations  per  minute.  Repeat  with 
lengths  of  36  cm.  and  25  cm. 

Record  all  observations  in  tabular  form  near  the  top  of 
the  left-hand  page. 

OBSERVATIONS 

Vibrations  per  minute,  bob  wood,  length  100  cm.,  arc 

small 

Vibrations  per  minute,  bob  metal,  length  100  cm.^  arc 
small  . 


98 


LABORATORY  EXERCISES 


ions  per  minute,  bob  metal,  length  100  cm.,  arc 

large  .............. 

Vibrations  per  minute,  bob  metal,  length  50  cm.,  arc 

small  .............. 

Vibrations  per  minute,  bob  metal,  length  36  cm.,  arc 

small  .............. 

Vibrations  per  minute,  bob  metal,  length  25  em.,  arc 

small  ..........     .... 


Make  a  drawing  of  your  apparatus  and  describe  briefly 
how  the  experiment  was  done. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page  and  directly  below  make  all  the  calcula- 
tions called  for. 

CALCULATED  RESULTS 


LENGTH 

PLRIOD 

100  cm. 

50cm. 

36cm. 

• 

25  cm. 

Conclusion: 

(a)  Does  the  mass  of  the  pendulum  affect  the  period  ? 
(6)  Does  the  amplitude  (if  comparatively  small)  affect 
the  period  ?  (c)  Is  there  any  simple  relation  between  the 
period  and  the  length  ?  between  the  square  of  the  period 
and  the  length  ? 


THE  INCLINED  PLANE  99 

EXPERIMENT    27 

The  Inclined  Plane 

OBJECT,  (a)  To  compare  the  work  done  in  raising  a  load  by 
means  of  an  inclined  plane  and  in  raising  it  vertically;  (b)to 
determine  the  mechanical  advantage  from  the  length  and  height  of 
the  plane. 

Note.  —  Only  the  case  when  the  force  is  parallel  to  the  plane  is  con- 
sidered in  this  experiment. 

APPARATUS.  Inclined  plane  properly  supported  ;  car  with  cord 
attached ;  500-gram  weight  or  other  load ;  spring  balance  (2000  g.). 

Introductory : 

Safe  movers  roll  a  safe  into  a  wagon  along  a  sloping 
plank.  Does  this  require  less  force  than  to  lift  the  safe 
directly  into  the  wagon  ?  Is  less  work  done  by  rolling  it 
up  the  incline  than  by  lifting  it  directly  ?  The  plank  is 
an  example  of  the  use  of  the  inclined  plane.  We  wish  to 
answer  the  above  questions  by  using  a  car  on  an  inclined 
board  in  the  laboratory.  We  also  wish  to  find  out  the 
mechanical  advantage  of  the  plane.  This  is  the  number 
which  is  obtained  by  dividing  the  resistance  by  the  effort. 
In  the  inclined  plane  the  mechanical  advantage  may  be 
found  also  from  the  dimensions  of  the  plane.  We  shall 
seek  to  find  what  dimensions  are  used  and  what  division  is 
made  to  obtain  the  mechanical  advantage. 

Experimental : 

An  iron  car  loaded  with  a  500-gram  weight  will  be  used 
and  it  is  to  be  pulled  up  an  inclined  plane  by  means  of  a 
cord  attached  to  a"  spring  balance.  This  balance  thus 
measures  the  force  employed  to  draw  the  car  up  the  plane. 


100 


LABORATORY  EXERCISES 


The  combined  weight  of  the  car  and  its  load  is  the  weight 
lifted  by  the  use  of  the  plane.  It  may  be  found  with  the 
spring  balance.  The  dimensions  of  the  plane  are  to  be 
measured,  as  shown  in  Fig.  39. 

Correction  is  to  be  made  for  some  friction.  This  may 
be  eliminated  by  averaging  the  reading  of  the  balance 
when  the  car  is  moving  uniformly  up  the  incline  with  the 


Fig.  39. 

reading  when  it  is  moving  uniformly  down  the  plane. 
Decide  in  each  case  whether  the  friction  is  a  help  or  a  hin- 
drance. The  work  done  along  the  plane  is  measured  by 
the  product  of  the  balance  reading  and  the  length  of  the 
plane  (to  A).  The  work  done  in  raising  the  weight  an 
equal  distance  is  measured  by  the  product  of  the  weight 
lifted  and  the  height  of  the  plane  (at  A). 

Record  the  observations  in  tabular  form  near  the  top  of 
the  left-hand  page. 

OBSERVATIONS 


Weight  of  car  and  load    .     . 
Force  required,  car  ascending 
Force  required,  car  descending 
Length  of  plane      .... 
Height  of  plane      .... 


9- 
9- 

cm. 
cm. 


THE  INCLINED  PLANE  101 

Make  a  simple  sketch  of  your  apparatus  and  write  a 
short  description  of  the  method  of  the  experiment. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 

Average  force  used g. 

Work  =  weight  lifted  X  height  of  plane    .     .     ,.        g.cm. 
Work  =  f  orce  x  length  of  plane g.cm. 

Mechanical  advantage  =  — ^ — •     .'.... 
force 

Length  of  plane 
Height  of  plane 

Conclusion : 

(a)  Compare  work  done  in  lifting  the  load  vertically 
from  the  table  to  the  level  of  A,  with  the  work  done  in 
raising  it  the  same  vertical  distance  by  rolling  it  along  the 
plane.  (J)  What  relation  between  the  height  and  length 
of  the  plane  equals  the  mechanical  advantage  ? 


102  LABORATORY   EXERCISES 


EXPERIMENT   28 

Pulleys 

OBJECT.  To  study  the  operation  of  pulleys  and  to  find  theii 
mechanical  advantage. 

APPARATUS.  1  single  fixed  pulley  and  1  double  fixed  pulley 
with  stems  for  clamping  or  attaching ;  single  movable  pulley ;  an 
additional  movable  pulley  or  a  movable  double  pulley  with  hooks 
for  suspending  pan  or  weights ;  support  for  fixed  pulley ;  balance 
pan1;  metric  weights ;  spring  balance  (250  g.) ;  meter  stick;  light, 
strong  flexible  cord  (fish  line). 

Introductory : 

The  block  and  tackle  is  a  familiar  sight  in  large  cities, 
as  it  is  used  for  moving  pianos  and  safes  in  and  out  of  high 
buildings.  In  the  country  it  is  used  for  pulling  stumps 
and  handling  logs.  On  the  water  front,  the  pulley  in 
some  form  or  combination  is  employed  for  loading  the 
heaviest  articles  of  the  cargo. 

Pulleys  would  not  be  so  widely  used  unless  they 
brought  some  mechanical  gain  to  their  users.  The  me- 
chanical advantage  of  a  machine  may  rest  in  changing 
either  the  direction  or  the  magnitude  of  the  force  applied 
to  it.  Wherein  lies  the  gain  when  pulleys  are  used? 

1  The  balance  pan  for  Part  (a)  is  made  by  first  finding  with  a  sensitive 
spring  balance  the  error  in  indicated  weight  arising  from  the  use  of  the 
balance  tested  in  an  inverted  position.  The  pan  is  made  from  thin  sheet 
copper  and  holes  punched  in  the  corners  for  the  fine  copper  wire  used  as 
suspension  cords.  The  weight  of  the  pan  and  its  suspension  should  equal 
the  weight  error  found  for  the  balance.  It  can  be  adjusted  by  filing  or 
punching. 


PULLEYS  103 

Experimental : 

(a)  The  Fixed  Pulley.     A  spring  balance  should  be  used 
with  the  hook  downward,  as  the  weights  of  the  hook  and 
the  drawbar  were  acting  on  the  spring  when 
the  mark  for  the  zero  point  was  located.     In 
an   inverted   position   the   balance  will   not 
read  correctly.     To  compensate  for  the  error 
arising  in  this  manner,  in  this  experiment, 
the  balance  pan  with  its  supporting  cords  has 
been  made  equal  in  weight  to  the  drawbar 
and  hook. 

The  apparatus  should  be  arranged  as  in 
Fig.  40.  A  weight  is  placed  in  the  pan  and 
the  spring  balance  is  pulled  vertically  down- 
ward so  as  to  raise  the  load  at  a  steady  rate, 
the  force  or  effort  necessary  being  read  at 
the  same  time  on  the  spring  balance.  Then  the  balance 
reading  is  again  taken  as  the  load  descends  at  a  uniform 
rate.  The  friction  increases  the  balance  reading  as  the 
load  ascends  and  decreases  the  reading  for  the  load  de- 
scending. An  average  of  the  two  readings  may  be  con- 
sidered as  the  force  or  effort  which  will  just  equal  the 
resistance  to  be  overcome  before  the  load  will  move. 

Take  readings  with  100  grams  and  200  grams  as  the 
loads,  and  record  in  tabular  form.  Note  the  distance 
through  which  the  load  is  raised  as  compared  With  the 
distance  through  which  the  effort  moves.  Compare  the 
load  with  the  effort.  What  is  the  only  mechanical  gain  in 
using  a  single  fixed  pulley  ? 

(6)  Single  Movable  Pulley.  The  apparatus  is  arranged 
as  in  Fig.  41.  The  total  load  in  this  case  includes  the 
weight  of  the  pan  and  the  weight  of  the  pulley  block. 
These  are  weighed  separately  and  the  weights  recorded. 


104 


LABORATORY  EXERCISES 


Readings  are  made  with  the  100-gram  and  the  200-gram 
weights  as  in  (a).     How  does  the  distance  through  which 
total  load  (resistance)  moves  compare 
with  the  effort  distance?     What  is  the 


Fig.  41. 


Fig.  42. 


Fig.  43. 


mechanical  advantage  of  a  single  movable  pulley  ?  Wliat  is 
sacrificed  to  gain  this  ? 

(c)  Combinations  of  Pulleys. —  A  single  fixed  and  a 
single  movable  pulley  are  arranged  as  in  Fig.  42.  This 
is  the  arrangement  used  in  the  movable  scaffolds  of 
house  painters.  Only  one  set  of  readings  is  made  —  that 
with  a  load  of  200  grams.  What  additional  advantage 
does  this  combination  of  pulleys  have  over  the  single  movable 
pulley  ? 

Next,  two  fixed  pulleys  (a  double  pulley)  and  a  single 
movable  pulley  are  combined  by  the  proper  adjustment  of 
cords.  Readings  are  taken  with  the  200-  and  the  500-gram 
weights.  The  vertical  distance  through  which  the  load 
moves  from  the  table  top  is  carefully  measured  as  is 
also  the  distance  covered  by  the  effort  at  the  same  time. 
Note  also  the  number  of  cords  which  support  the  movable 
block. 

Then  a  fixed  pulley  is  combined  with  two  movable  pulleys 


PULLEYS 


105 


(or  a  double  pulley),  and  a  similar  set  of  readings  taken 
with  weights  of  200  and  500  grams. 

Make  for  (a),  (5.),  and  (c)  simple  diagrams  showing  the 
arrangement  of  the  load,  the  pulleys,  and  the  spring  balance. 
Indicate  clearly  the  number  of  cords  which  support  the 
movable  pulley  blocks. 

Write  simple  descriptions  of  the  work  done  in  each 
part  of  the  experiment,  shortening  the  descriptions  by 
references  to  the  diagrams. 

OBSERVATIONS 


TRIALS 

PULLEYS  USED 

WEIGHTS  OF 

BALANCE  READING 

Load 

Pan 

Movable 
Block 

Up 

Down 

1  and    2 

1  fixed 

100  g. 





3  and    4 

1  fixed 

200  g. 

— 



5  and    6 

1  movable 

100  g. 

7  and    8 

1  movable 

200  g. 

9  and  10 

1  fixed  and  1  mov. 

200  g. 



11  and  12 

2  fixed  and  1  mov. 

200  g. 



13  and  14 

2  fixed  and  1  mov. 

500  g. 

— 

etc. 

etc. 

etc. 

For  Part  (<?)  only ;    Trials  11  to  18 


NUMBER  OF 
TRIALS 

RESISTANCE 
(Total  Load) 

EFFORT 

(Average  Balance) 

DISTANCE  MOVED  THROUGH 

Resistance 

Effort 

11  and  12 

13  and  14 

15  and  16 

17  and  18 

106 


LABORATORY  EXERCISES 


Except  in  Part  (a),  the  total  load  (resistance)  is  the 
sum  of  the  weights  on  the  pan,  the  weight  of  the  pan,  and 
the  weights  of  the  movable  blocks  used.  The  average  of 
the  two  balance  readings  in  each  trial  is  the  effort.  The 
mechanical  advantage  of  a  machine  is  denned  as  the  re- 
sistance divided  by  the  effort.  Record  these  calculated 
results  in  a  table  at  the  top  of  the  right-hand  page. 

CALCULATED  RESULTS 


TRIALS 

PULLEYS 

USED 

RESISTANCE  (R) 
(Total  Load) 

EFFORT  (E) 
(Average 
Balances) 

MECIIANICAI. 
ADVANTAGE 
R-*-E 

COKDS  SUPPORTING 
MOVABLE  BLOCK 

Discussion: 

Under  this  heading  on  the  right-hand  page  (or  the 
second  right-hand  page)  answer  the  italicized  questions 
occurring  in  the  experimental  directions. 

Conclusion: 

After  comparing  in  each  case  the  number  representing 
the  mechanical  advantage  with  the  number  of  cords  sup- 
porting the  movable  block  or  blocks,  answer  the  following 
question: 

How  may  the  mechanical  advantage  of  a  set  of  pulleys 
be  stated  in  terms  of  the  machine's  construction? 


THE  WHEEL  AND  AXLE  107 

EXPERIMENT   29 

The  Wheel  and  Axle 

OBJECT.  To  study  the  operation  of  the  wheel  and  axle  and  to 
find  its  mechanical  efficiency. 

APPARATUS.  Wheel  and  axle  with  several  diameters  ;  metric 
weights  (500  g.  and  1000  g.)  ;  spring  balance  (2000  g.)  in  case 
apparatus  has  not  an  exact  simple  ratio ;  fish  line ;  stand  and 
clamp  for  wheel  and  axle  in  case  it  is  not  mounted  on  its  own 
base  ;  pair  of  calipers  (or  a  pencil  compass)  is  convenient  for 
measuring  the  radii ;  meter  stick. 

Introductory : 

The  windlass  is  used  to  lift  a  bucket  from  a  well  or 
dirt  from  an  excavation.  Several  men  on  a  capstan  can 
pull  out  of  the  water  a  heavy  anchor  which  they  could  not 
lift  with  their  hands  from  the  deck  of  the  vessel.  The 
devices  for  accomplishing  these  rather  difficult  tasks  are 
applications  of  the  wheel  and  axle,  one  of  the  simple 
machines.  In  the  illustrations  just  given,  a  lesser  effort 
overcomes  a  larger  resistance,  or  there  is  a  mechanical  ad- 
vantage greater  than  one.  Upon  what  does  the  mechani- 
cal advantage  of  a  wheel  and  axle  depend  ? 

Experimental : 

One  cord  is  attached  to  the  axle  and  another  cord  to 
the  wheel.  On  the  axle  cord  is  attached  the  load  (resist- 
ance^ ;  on  the  wheel  cord  are  attached  weights  which  act 
as  the  effort  and  just  balance  the  load.  When  the  weights 
on  the  two  cords  are  in  equilibrium,  the  slightest  pull  on 
the  cord  in  either  direction  should  make  the  weights  run 
freely  up  and  down  at  a  gentle  rate. 

The  weights  may  be  attached   by  a  slip  noose  in  the 


108 


LABORATORY  EXERCISES 


free  end  of  the  cord.     The  first  load  may  be  conveniently 

1000  grams.  The  distances  traveled  by  the  effort  and 
the  resistance  in  the  same  time  are  measured 
with  a  meter  stick.  The  radius  of  the  axle 
and  the  radius  of  the  wheel  are  also  deter- 
mined. All  these  measurements  are  to  be 
recorded  in  tabular  form  near  the  top  of 
the  left-hand  page. 

At  the  direction  of  the  instructor,  meas- 
urements with  additional  loads  are  made. 
In  case  there  are  several  wheels  on  the  axle, 
one  of  the  smaller  wheels  may  be  taken  for 
a  new  axle.  For  some  of  the  measurements 

it  may  prove  necessary  to  use  a  spring  balance  in  place 

of  the  effort  weight. 

OBSERVATIONS 


Fig.  44. 


NUMBER  OP 

LOAD  ON  AXLE 

EFFORT  ON 

i:\iins  OF 

RADIUS  OF 

TRIAL 

(Resistance) 

WHEEL 

AXLE 

WHEEL 

1 

1000  g. 

2 

etc. 

etc. 

For  Two  Readings  Only 


NUMBER  OF 
TRIAL 

LOAD 
(Resistance) 

EFFORT 

DISTANCE  MOVED  THROUGH 

Resistance 

Effort 

Make  a  drawing  of  the  wheel  and  axle  used  and  write  a 
simple  description  of  how  the  experiment  was  done. 


THE  WHEEL  AND  AXLE 


109 


The  mechanical  advantage  of  a  simple  machine  like  the 
wheel  and  axle,  is  the  ratio  of  the  resistance  to  the  effort. 
Calculate  this  for  each  trial.  Also  find  in  each  case  the 
ratio  of  the  radius  of  the  wheel  to  the  radius  of  the  axle. 
Place  all  the  calculated  results  in  tabular  form  at  the  top 
of  the  right-hand  page. 

CALCULATED  RESULTS 


NUMBER  OF 

RESISTANCE  (R) 

EFFOBT  (E) 

MECHANICAL 

RADIUS  WHEEL 

TKIAL 

(Load) 

Discussion : 

What  is  sacrificed  in  gaining  the  mechanical  advantage 
of  the  wheel  and  axle  ? 

Conclusion : 

Complete   the   following  statement:     The   mechanical 
advantage  of  the  wheel  and  axle  may  be  stated  in  terms 

of  its   construction   as  the  ratio  of  the • 

to  the  


110  LABORATORY  EXERCISES 

EXPERIMENT    30 

Mechanical  Efficiency  of  Machines 

OBJECT.  —  To  find  the  mechanical  efficiency  of  an  inclined  plane, 
a  set  of  pulleys,  and  a  wheel  and  axle. 

APPARATUS.  As  designated  for  the  inclined  plane  (page  99), 
for  the  pulley  (page  102),  and  for  the  wheel  and  axle  (page  107). 

In  the  experiments  on  those  machines,  measurements  were 
made  and  tabulated  which  will  serve  for  this  experiment. 

Commercial  block  and  tackle  with  necessary  weights  in  case 
Part  (b)  is  to  be  done. 

Introductory : 

The  rapid  growth  of  the  manufacturing  industries  in 
the  United  States  has  been  due  in  large  part  to  the  develop- 
ment of  efficient  machinery.  To  be  efficient,  a  machine 
must  return,  in  some  form  of  useful  output,  a  large  part  of 
the  energy  applied  to  it.  Machines  which  waste  too  much 
of  the  applied  energy  in  friction,  in  loss  of  motion,  or  in 
other  ways,  are  condemned  to  the  scrap  heap  when  a 
more  efficient  machine  for  the  same  purpose  is  devised. 
Calculations  of  the  efficiency  of  complicated  machinery 
are  difficult  even  for  a  competent  mechanical  engineer, 
but  a  student  can  learn  from  the  inclined  plane,  the  pulley, 
and  the  wheel  and  axle,  the  main  factors  in  the  efficiency 
of  any  machine.  These  factors  are  in  accordance  with 
the  law  of  work,  —  "  the  amount  of  work  put  into  a  perfect 
machine  equals  the  work  gotten  out  of  it." 

The  mechanical  efficiency  of  a  machine  is  the  percentage 
of  total  work  done  on  the  machine  which  proves  useful. 

Experimental : 

(a)  The  instructor  may  direct  the  use  of  the  readings 
obtained  in  the  experiments  on  the  inclined  plane,  the 


MECHANICAL  EFFICIENCY  OF  MACHINES      111 

pulley,  or  the  wheel  and  axle.  In  all  cases,  the  effort 
readings  used  must  be  ones  taken  while  the  weight  (re- 
sistance) is  being  raised,  without  correction  for  friction. 
These  are  the  conditions  under  which  a  machine  does  use- 
ful work. 

The  weight  raised,  the  height  of  the  plane,  the  force 
with  load  ascending,  and  the  length  of  the  plane  are  the 
readings  to  be  taken  from  the  inclined  plane  experiment. 

It  should  be  noted  with  regard  to  the  inclined  plane 
that  the  load  (resistance)  moves  through  a  useful  distance 
equal  to  the  height  of  the  plane  while  the  effort  is  moving 
the  length  of  the  plane.  The  effort  is  the  force  used  with 
the  load  ascending. 

In  the  pulley  and  the  wheel  and  axle  experiments,  most 
of  the  readings  necessary  for  this  experiment  were  tabulated 
in  the  second  table  of  observations.  The  effort  reading  to 
be  taken  from  the  pulley  experiment  is  not  the  "  average 
balance,"  but  the  balance  reading  with  the  load  ascending, 
recorded  in  the  first  table  of  observations. 

The  observations  taken  from  previous  experiments 
should  be  again  tabulated  near  the  top  of  the  left-hand 
page  used  for  this  experiment.  Any  new  observations 
made  at  the  direction  of  the  instructor  may  be  tabulated 
in  the  same  form. 

(6)  During  the  laboratory  hour,  if  the  instructor  so 
directs,  a  test  will  be  made  on  the  efficiency  of  a  commer- 
cial block  and  tackle  with  as  large  a  load  as  is  safe  and 
desirable.  The  students  designated  by  the  instructor  to 
make  the  test  will  report  the  results  to  the  class.  Com- 
parison can  then  be  made  between  the  school  apparatus, 
designed  to  show  the  law  of  work,  and  commercial  appa- 
ratus, made  to  stand  the  wear  and  tear  of  actual  service. 

In  a  perfect  machine,  the  amount  of  work  obtained 
from  it  equals  the  amount  of  work  put  into  it,  i.e.  resist- 


112 


LABORATORY  EXERCISES 


ance   x  resistance    distance  =  effort   x  effort    distance. 
Calculate  these  two  products  for  each  observation. 

Then  calculate  the  mechanical  efficiency  of  each  machine 
from  the  two  products,  recalling  that 

^-^  .  useful  work  (work  output") 

Efficiency  =  —  -^* 

•  total  work  (work  input) 

OBSERVATIONS 


MACHINE 

RESISTANCE 

EFFORT 

ISTANCE   MO\E 

D   THROUGH 

(Load  or  Weight  lifted) 

(Force  applied) 

Resistance 

Effort 

At  the  top  of  the  right-hand  page  tabulate  the  results 
of  all  calculations. 

CALCULATED  RESULTS 


MACHINE 

USEFUL  WORK 
(Resistance  X 
Resistance  Distance) 

TOTAL  WORK 
(Effort  X 
Effort  Distance) 

MKCH.  EFFICENCY 
/Useful  Work\ 

^  Total  Work/ 

Discussion : 

What  may  make  the  mechanical  efficiency  vary  in  dif- 
ferent observations  of  the  same  machine? 

Conclusion : 

The  average  mechanical  efficiency  found  from  my  ob- 
servations was  for   the   inclined   plane %,  for  the 

pulleys °/ci  and  for  the  wheel  and  axle  ......  %. 

(state  combination  used) 


COEFFICIENT  OF  FRICTION  113 

EXPERIMENT  31 

Coefficient  of  Friction 

OBJECT.  To  determine  the  ratio  of  the  friction  between  two 
surfaces  to  the  pressure  holding  them  together. 

APPARATUS.  Rectangular  wooden  block ;  board  with  uniform 
surface,  with  support  for  use  as  inclined  plane ;  spring  balance 
(2000  g.)  ;  fish  line  ;  block  of  weights ;  meter  stick. 

Introductory : 

Heavy  loads  on  a  wagon  press  down  and  increase  the 
friction  at  the  axles.  The  ratio  between  the  friction  and 
the  pressure  causing  it,  is  called  the  coefficient  of  friction. 

This  fraction  has  different  values  according  to  the 
kinds  of  surface  in  contact.  For  instance,  there  is  more 
friction  between  rubber  soles  and  a  polished  floor  than 
between  leather  soles  and  the  same  floor.  The  man  with 
the  rubber  soles  can  walk  up  a  steeper  plank,  but  even  he 
will  begin  to  slip  when  the  pitch  of  the  plank  is  increased 
to  a  certain  definite  angle.  The  leather  soles  slip  at 
a  smaller  definite  angle  of  pitch. 

The  coefficient  of  friction  may  be  found,  either  by 
measuring  both  friction  and  pressure  directly,  or  by  find- 
ing the  angle  of  elevation  of  the  surface  of  one  body,  at 
which  the  weight  of  a  second  body  will  just  cause  the 
latter  to  slip  down  the  inclined  surface  of  the  first. 

Experimental : 

(a)  A  hard  wood  block,  with  various  weights  upon  it, 
is  dragged  over  the  surface  of  a  smooth  horizontal  board 
by  means  of  a  cord  attached  to  the  block  and  to  a  spring 
balance.  If  the  block  is  kept  moving  at  a  uniform  speed, 


114 


LABORATORY  EXERCISES 


the  reading  of  the  balance  will  show  the  amount  of  the 
friction  between  the  surfaces.     The  pressure  between  the 


Fig.  45. 

surfaces  is  the  weight  of  the  block  plus  the  load  placed 
upon  it.  Several  weights  ranging  from  100  to  1000  grams 
should  be  used  to  load  the  block.  From  these  readings 
the  coefficient  of  friction  may  be  found  by  dividing  the 
friction  by  the  pressure  causing  it. 

(5)  Using  the  same  block  and  board,  with  a  support  to 
adjust  the  board  to  any  desired  inclination,  the  board  may 


=-- 


Fig.  46. 

be  raised  gradually  until  the  unloaded  block  will  just 
slide  down  with  uniform  motion  if  the  board  is  constantly 
tapped  with  the  finger.  This  angle  is  called  the  limiting 


COEFFICIENT  OF  FRICTION  115 

angle  of  friction.  Referring  to  Fig.  46,  AC  and  BC  should 
be  measured. 

When  a  body  rests  on  an  inclined  plane,  its  weight,  w, 
is  resolved  into  two  component  forces.  One  of  these,  p,  is 
perpendicular  to  the  plane  and 
produces  pressure  upon  it. 
The  other  component  /  acts  par- 
allel to  the  plane  and  toward  the 
lower  end.  As  this  is  the  only 
component  of  the  force  that  acts 
in  the  direction  in  which  the  Fi  47 

body  on  the  plane  may  move,  it 

is  evident  that  only  this  force  needs  to  be  balanced  to 
keep  the  body  from  moving  down  the  plane.  Therefore, 
at  the  limiting  angle,  the  component  /  of  the  weight  w, 
as  it  urges  the  block  down  the  plane,  just  balances  the 
friction. 

It  will  be  readily  seen  (Fig.  47)  that  the  triangles  fwp' 

and  AB  0  are  similar.     Hence,  ^  =-—-.      But  ^  is   the 

p     AC  p 

friction  divided  by  the  pressure  and  is,  therefore,  the 
quantity  we  seek.  Its  value,  then,  may  be  calculated  by 
dividing  the  height  of  the  plane  by  the  length  of  the  base. 
.  Record  the  readings  in  tabular  form  near  the  top  of  the 
left-hand  page. 

OBSERVATIONS 
Part  (a)  : 

1  2  Etc. 

Total  pressure  (block  and  weight)  ._  ._  g. g.  __  __  g. 

Reading  of  balance     ....     g. g. g. 

Part  (b)  : 

Height  of  plane cm. 

Length  of  base '          cm. 


116  LABORATORY  EXERCISES 

Make  a  clear  outline  drawing  of  your  apparatus  and 
briefly  describe  your  work  in  both  (a)  and  (5). 

Place  the  calculated  results  in  tabular  form  at  the  top 
of  the  right-hand  page. 

CALCULATED  RESULTS 
Part  (a)  : 

Coefficient  of  friction  (f™tion  ] 
\pressurej 

123  Etc.  Average 

Part  (5)  : 

Coefficient  of  friction    ^r-    ..... 


Discussion  : 

Is  the  coefficient  of  friction  dependent  upon  the  load  ? 
Show  why  the  ratio  of  the  height  to  the  base  of  the  in- 
clined plane  at  the  limiting  angle  is  equal  to  the  coefficient 
of  friction. 

Conclusion  : 

The  coefficient  of  friction  between    _____  and  ______  is 

(name  materials) 


EXPERIMENT  32 

Vibrations  of  a  Tuning  Fork 

OBJECT.    To  determine  the  frequency  of  a  given  tuning  fork. 

APPARATUS.  A  low  frequency  tuning  fork  (not  over  128  V.P.S.) 
with  considerable  amplitude  of  vibration,  preferably  made  of  bell 
metal,  and  with  a  bristle  or  stylus  attached  ;  oval  piece  of  wood ; 
glass  plate  smoked  ;  pendulum  beating  known  fraction  of  a  second, 
provided  wifh  a  stylus ;  rigid  clamps  for  tuning  fork  and  pendu- 


VIBRATIONS  OF  A  TUNING  FORK  117 

lum  ;  holder  and  track  for  glass  plate ;  candle,  or  cake  of  "  Bon 
Ami." 

Note. — Apparatus  dealers  furnish  sets  of  the  above  ap 
paratus. 

Introductory : 

A  knowledge  of  the  number  of  vibrations  correspond- 
ing to  each  musical  note  is  essential  to  the  understanding 
of  the  Physics  of  Sound.  While  the  ear  may  be  trained 
to  estimate  very  closely  the  pitch  of  the  tuning  fork,  the 
eye  is  not  quick  enough  to  count  its  vibrations.  By  pro- 
viding the  fork  with  a  tracing  point  and  by  drawing  pre- 
pared glass  or  paper  under  the  fork  at  right  angles  to  the 
direction  in  which  the  fork  is  vibrating,  each  complete  back 
and  forth  vibration  of  the  fork  will  be  represented  by  a 
wave-shaped  mark.  If  a  pendulum  provided  with  a  trac- 
ing point  is  so  placed  that  it  also  vibrates  across  the  glass, 
the  distance  the  glass  moved  during  the  known  period  of 
the  pendulum  is  also  recorded.  Then  the  number  of  vi- 
brations of  the  tuning  fork  in  that  period  may  be  counted. 

Experimental : 

The  best  way  of  preparing  the  glass  is  to  rub  over  it  a 
thin  coat  of  "Bon  Ami"  or  of  whiting  and  alcohol,  and 
allow  it  to  dry.  The  apparatus  should  then  be  carefully 
inspected  and  adjusted  so  that  the  tracing  points  of  both 
the  fork  and  the  pendulum  will  sweep  across  the  plate  in 
as  nearly  the  same  line  as  they  can  without  interfering 
with  each  other.  The  tracing  points  must  bear  on  the 
surface  hard  enough  to  scratch  away  the  coating,  but  not 
with  pressure  enough  to  check  the  motion  of  either  fork 
or  pendulum.  This  may  be  tested  by  setting  each  in 
vibration  with  the  glass  at  rest. 

The  fork  is  best  set  vibrating  by  placing  between  the 


118  LABORATORY  EXERCISES 

prongs  an  oval  stick  of  wood,  thick  enough  to  spread  the 
prongs  the  desired  amount,  and  then  suddenly  pulling  it 
out. 

When  all  adjustments  are  made,  set  pendulum  and 
tuning  fork  in  vibration  and  with  a  steady,  even  motion 
draw  the  glass  along  the  track  at  such  a  rate  as  to  have 


Fig.  48.     A  Vibrograph. 


at  least  one  complete  swing  of  the  pendulum,  back  and 
forth,  recorded  on  the  glass.  Remove  the  glass,  to  permit 
others  to  use  the  apparatus. 

The  number  of  complete  wave  forms  traced  by  the  fork 
between  two  successive  points  where  the  pendulum  wave 
crosses  the  tuning  fork  wave,  is  the  number  of  vibrations 
made  by  the  tuning  fork  in  the  period  of  the  pendulum. 

Place  in  tabular  form,  near  the  top  of  the  left-hand  page, 
the  time  of  the  pendulum  period  and  the  number  of  vibra- 
tions recorded  each  time  during  that  period. 

OBSERVATIONS 

Trial !  2  3  4 

Observed  vibrations       .     

Period  of  pendulum      .     — '.. 

Number  of  fork   .     .     .     


VIBRATIONS  OF  A  TUNING  FORK  119 

Make  a  simple  drawing  of  your  apparatus  and  describe 
briefly  the  essentials  of  the  method. 

Calculate  the  average  number  of  vibrations  for  the 
period  of  the  pendulum,  and  from  the  average  find  the 
number  of  vibrations  per  second.  Record  the  calculated 
results  at  the  top  of  the  right-hand  page. 

CALCULATED  RESULTS 

Average  number  of  vibrations  in sec.  was  .     .      

Frequency  of  fork  (vibrations  per  second)     .     .     .     

Discussion : 

(a)  Explain  fully  why  a  complete  wave  trace  of  the 
fork  stands  for  one  vibration  of  the  fork. 

(6)  Why  does  a  half  wave  trace  stand  for  the  period 
of  the  pendulum  ? 

Conclusion : 

The  frequency  of  fork  No. is vibrations  per 

second. 


120  LABORATORY  EXERCISES 

EXPERIMENT   33 

The  Velocity  of  Sound  in  Air 

OBJECT.  To  determine  the  approximate  velocity  of  sound  in  the 
open  air  at  the  existing  conditions. 

APPARATUS.  Pendulum  (f  sec.)  with  large-faced  bob a  and 
mounted  in  a  shallow  box  ;  pair  of  field  glasses  ;  measuring  tape  ; 
two  short  pieces  of  board ;  thermometer. 

Introductory : 

A  flash  of  lightning  is  usually  seen  before  the  thunder, 
the  sound  accompanying  the  electric  discharge,  is  heard. 
The  steam  escaping  from  the  whistle  on  a  distant  loco- 
motive may  be  noticed  several  seconds  before  the  sound 
reaches  our  ears.  The  flash  of  a  gun  is  evident  before 
the  sound  of  the  discharge  is  heard.  All  these  illustra- 
tions show  that  sound  travels  much  more  slowly  than 
light,  and  that  an  appreciable  interval  is  required  for  a 
sound  to  travel  any  considerable  distance.  Since  light 
has  such  great  velocity,  the  time  required  for  it  to  travel  a 
part  of  a  mile  is  not  measurable  by  any  ordinary  means, 
while  the  comparatively  slow-traveling  sound  takes  a 
noticeable  time  for  the  same  distance.  These  relative 
velocities  make  possible  a  simple  method  for  determining 
the  number  of  feet  per  second  traveled  by  a  sound. 

Experimental : 

Mount  the  pendulum  beating  three  fourths  of  a  second 
in  a  shallow  wooden  box  with  the  cover  removed.  Stretch 

1  In  case  a  pendulum  with  a  brass  bob  is  not  available,  a  pendulum 
may  be  made  with  a  5-lb.  slotted  weight  and  a  wooden  bar,  or  a  good  bob 
could  be  cast  of  lead  with  a  small  brass  curtain  rod  inserted,  in  the  cover 
of  a  coffee  tin  or  lard  pail.  Whatever  large-faced  bob  is  used,  one  face 
should  be  painted  a  blue  similar  to  that  used  in  the  enameled  street  signs. 


THE  VELOCITY  OF  SOUND  IN  AIR  121 

across  the  box  opening  an  opaque  white  cloth  and  in  it 
make  a  hole  the  shape  and  size  of  the  pendulum  bob  at 
the  center  of  its  vibration.  At  the  back  of  the  hole  and 
on  the  bottom  of  the  box  arrange  a  white  background. 
The  exposed  face  of  the  bob  should  be  painted  blue,  since 
this  color  will  be  readily  seen  as  the  bob  swings  across 
the  opening. 

Set  the  pendulum  about  500  feet  away,  so  placed  that  the 
bob  of  the  pendulum  is  several  feet  from  the  ground.  One 
student  is  stationed  at  the  box  with  two  short  boards  and 
strikes  them  together  so  as  to  produce  a  sharp  sound  every 
time  the  bob  is  at  the  center  of  its  swing. 

Observers  should  move  either  toward  or  away  from  the 
pendulum  until  a  position  is  obtained  where  the  successive 
sounds  produced  coincide  with  the  successive  swings  of 
the  bob  across  the  opening.  This  means  that  the  sound 
produced  at  the  center  of  one  beat  of  the  pendulum 
reaches  the  observer  at  the  center  of  the  next  beat.  Then 
during  the  time  of  one  beat,  the  sound  travels  the  distance 
of  the  pendulum  from  the  observer.  Field  glasses  will  be 
necessary  to  see  clearly  the  swing  of  the  bob  across  the 
opening. 

Make  one  determination  with  the  wind,  and  one  against 
it,  and  record  the  distances  as  measured  with  a  tape. 

Take  the  temperature  of  the  air  and  record  in  the  table 
of  observations. 

OBSERVATIONS 

Distance  of  observer  to  pendulum,  with  wind    .  ft. 

Distance  of  observer  to  pendulum,  against  wind          ft. 
Temperature  of  air °(7. 

Make  drawings  showing  how  the  pendulum  was  set  up 
and  describe  the  method  of  the  experiment. 


122  LABORATORY  EXERCISES 

CALCULATED  RESULTS 

Average  distance  traveled  by  sound  in  |  second  ft. 

Velocity  of  sound  per  second ft. 

Conclusion : 

The  velocity  of  sound  per  second  in  the  open  air  at °O. 


was 


EXPERIMENT   34 

Sympathetic  Vibrations 

OBJECT.  To  set  a  tuning  fork  into  vibration  by  sympathetic 
vibrations  with  another  fork  of  the  same  frequency. 

APPARATUS.  Two  tuning  forks  of  the  same  frequency,1  as 
256  V.P.S. ;  tuning  fork  of  different  frequency,  as  384  V.P.S. ; 
flat  cork  about  2"  in  diameter;  500-gram  weight  or  iron  ball 
with  fish  line  for  suspension  ;  support  for  hanging  weight. 

Introductory : 

When  the  loud  pedal  of  a  piano  is  pressed,  dampers  are 
lifted  from  the  strings  so  that  the  strings  can  vibrate 
freely.  Then  a  note  sung  into  the  piano  will  make  one 
wire  vibrate  in  response,  so  that  a  note  of  the  same  pitch 
can  be  heard.  The  sound  vibrations  produced  by  the 
human  voice  have  been  the  stimulus  to  the  production 
of  a  sound  by  the  vibration  of  one  of  the  piano  wires. 

1  Note  to  Instructor.  —  Two  forks  stamped  with  the  same  frequency 
number  will  rarely  vibrate  at  the  same  rate  without  filing  notches  in  the 
end  of  one  of  them.  Do  this  by  taking  two  forks  that  sound  nearly  alike 
and  than  raise  the  pitch  of  the  lower  (flat)  fork  by  filing  the  outer  end 
of  one  prong.  Then  stamp  or  file  an  identifying  number  on  the  handle 
of  both  forks.  Always  give  out  together  that  pair  of  forks  for  this 
experiment. 


SYMPATHETIC  VIBRATIONS  123 

Since  the  stimulating  sound  and  the  sound  produced  have 
the  same  pitch  (frequency  of  vibration),  this  is  a  case  of 
sympathetic  vibrations.  Tuning  forks  are  very  convenient 
instruments  for  studying  sympathetic  vibrations,  for  their 
rate  of  vibration  per  second  is  known.  Usually  the  fre- 
quency number  is  stamped  at  the  base  of  the  two  prongs. 

Experimental : 

(a)  Suspend  a  500-gram  weight  (or  a  ball  of  about  the 
same  weight)  by  a  light,  strong  cord  about  a  meter  in 
length. 

When  the  weight  is  at  rest,  give  it  a  light  tap  with  a 
lead  pencil,  noting  the  direction  in  which  the  weight  be- 
gins to  move  or  vibrate.  When  the  weight  is  at  the 
center  of  its  swing  and  moving  from  you,  tap  again.  Con- 
tinue in  this  manner  until  the  weight  has  received  about 
twenty  gentle  taps.  What  is  the  effect  upon  the  vibra- 
tions of  the  suspended  weight  ?  From  what  source  did 
the  weight  get  its  impulses  ? 

With  the  weight  again  at  rest,  give  it,  without  paying 
any  attention  to  the  intervals,  twenty  more  gentle  taps, 
hitting  the  weight  just  as  it  happens  to  be  coming  toward 
or  going  away  from  you.  What  is  the  effect  on  the  vi- 
bration of  the  weight  ?  Compare  the  regularity  in  time 
of  this  second  tapping  with  that  of  the  first.  What  rela- 
tion existing  between  the  regularity  cf  the  tapping  and  the 
vibration  of  the  weight,  caused  such  a  marked  effect  in  the 
first  case  f 

(ft)  The  following  directions  must  be  followed  exactly 
in  order  to  secure  the  desired  result.  Study  them  thor- 
oughly before  beginning  the  experiment.  Examine  the 
forks  to  see  that  the  same  number  is  marked  on  the  stem 
of  each. 

(1)    Hold  the  two  forks  by  the  stem,  not  allowing  the 


124  LABORATORY  EXERCISES 

fingers  to  touch  any  other  part  of  the  fork  (in  order  to 
avoid  heating). 

(2)  Set  the  fork  held  in  the  right  hand  into  vigorous 
vibration  by  striking  the  end  of  one  of  its  prongs  sharply 
against  a  cork  on  the  desk. 

(3)  Steady   the   fork   in   the  left   hand    by   allowing 
the  hand  to  rest  against  the  desk  with   the   fork   held 

horizontally. 

(4)  Bring  the  vibrating 
fork  into  a  position  paral- 
lel to  the  other  fork,  with 
Fig.  49.  the   prongs   extending  in 

an  opposite  direction  and 
the  two  forks  about  -Jg  of  an  inch  apart  (Fig.  49). 

(5)  After  the  forks  have  been  in  this  position  while 
you  count  three,  slowly  bring  the  left-hand   fork   near 
the   ear   and   determine   whether  it   has    been    set    into 
vibration. 

(6)  If  the  first  trial  has  not  been  successful,  repeat  the 
work. 

Apply  to  the  instructor  for  a  tuning  fork  of  different 
frequency  from  that  of  the  two  forks  used.  With  this 
fork  and  one  of  the  former  ones  repeat  the  experiment, 
noting  the  success  of  your  efforts. 

Make  a  drawing  showing  the  forks  in  the  position 
where  sympathetic  resonance  was  obtained.  Write  a  full 
description  of  the  experiment  and  its  results. 

Conclusion: 

Answer  the  italicized  question  in  Part  (a).  What  must 
be  true  of  the  frequencies  of  two  forks  in  order  that  one 
of  them  may  be  set  into  sympathetic  vibration  by  the  other? 


THE  WAVE  LENGTH  OF  A  SOUND  125 

EXPERIMENT   35 

The  Wave  Length  of  a  Sound 

OBJECT.  To  determine,  at  the  temperature  of  the  room,  the 
length  of  a  sound  wave  from  a  C  tuning  fork  (256  V.P.S.)- 

APPARATUS.  Glass  resonating-tube  about  12"  long  and  1"  to 
1^"  in  diameter,  with  lower  end  closed  by  a  1-hole  rubber  stopper 
carrying  a  glass  delivery  tube  with  rubber  connection  and  pinch- 
cock  between  the  two  sections  ;  beaker  ;  ring  stand  and  clamp  with 
jaws  lined  with  cork;  C  tuning  fork,  256  V.P.S.  ;  flat  cork  about 
2"  in  diameter. 

Introductory : 

When  a  prong  of  a  tuning  fork  is  vibrating,  the  prong 
makes  a  forward  and  a  backward  movement  in  completing 
one  vibration.  The  vibrating  prong  sets  the  adjacent 
air  vibrating  longitudinally,  and  finally  the  sound  wave 
reaches  our  ear.  By  using  a  glass  tube  with  the  lower 
end  closed  by  water,  we  get  a  vibrating  air  column  whose 
length  can  be  readily  measured.  When  the  vibrating  fork 
is  held  over  the  open  end  of  the  tube,  the  air  column 
within  is  set  into  vibration.  The  sound  wave  starting 
from  the  prong  travels  down  the  tube  to  the  water  surface, 
where  it  is  reflected  and  travels  back  again  to  the  vibrat- 
ing prong.  By  varying  the  length  of  the  air  column,  it  is 
found  that  a  column  of  certain  length  greatly  intensifies  or 
reenforces  the  sound  of  the  tuning  fork.  This  reenforce- 
ment  or  resonance  is  due  to  the  reflected  wave  adding  its 
sound  to  the  sound  being  produced  by  the  vibrating  prong. 
To  get  the  maximum  intensification  or  resonance,  the  im- 
pulse started  by  the  forward  movement  of  the  prong  must 
travel  down  the  tube  and  back  again  in  time  to  reenforce 
the  prong  in  its  backward  motion.  Thus  during  the  first 


126 


LABORATORY  EXERCISES 


half  vibration  of  the  prong,  the  sound  produced  by  it  has 
traveled  twice  the  length  of  the  air  column.  During  a 
whole  vibration  the  sound  would  travel  four  times  the  length 
of  the  air  column.  The  distance  traveled  by  a  sound, 
while  the  body  producing  it  is  making  one  vibration,  is 
the  wave  length  of  that  sound.  From  this  discussion  it 
can  be  seen  that  the  length  of  the  vibrating  air  column  is  one 
quarter  the  wave  length  of  the  sound  when  the  air  column  is 
adjusted  to  the  point  of  maximum  resonance. 

Experimental : 

Arrange  the  apparatus  as  in  Fig.  50.     To  avoid  disturb- 
ing sounds,  the  jaws  of  the  clamp  should  be  lined  with 
cork   and   the  delivery  tube  should 
«=C(         !  always  be  dipping  into  the  water  of 

the  beaker. 

Start  with  the  resonating  tube 
nearly  full  of  water,  and,  by  letting 
the  water  out  slowly  through  the  de- 
livery tube,  find  a  level  which  will 
give  the  strongest  reenforcement  of 
the  sound  emitted  by  the  fork.  In 
making  this  determination,  set  the 
fork  vibrating  loudly  by  striking  it  on 
the  large  cork,  and  hold  the  fork  just 
over  the  top  of  the  tube  with  the 
prongs  parallel  to  the  surface  of  the 
water.  In  case  too  much  water  runs 
out  of  the  resonating  tube,  pour  some 
^  back  from  the  beaker.  In  order  to 
Fi£-  SO-  determine  whether  it  is  your  air 

column    or    that    of   your   neighbor 

which  is  sounding,  keep  moving  your  fork  over  the  mouth 
of  the  tube  and  then  away  from  the  tube. 


c-I 


THE  WAVE  LENGTH  OF  A  SOUND  127 

When  the  precise  level  for  the  loudest  resonance  is 
found,  measure  in  inches  the  length  of  the  air  column  for 
this  position  and  the  internal  diameter  of  the  tube. 

Keeping  the  same  fork,  exchange  the  rest  of  your 
apparatus  for  that  of  another  student  and  make  a  second 
determination  of  the  level  of  loudest  resonance.  Measure 
as  before  and  record. 

In  the  tabular  form  near  the  top  of  the  left-hand  page 
record  the  vibration  number  stamped  on  the  fork  and  also 
the  temperature  of  the  room. 

OBSERVATIONS 


Length  of  resonant  air  column 

Internal  diameter  of  tube 

Frequency  of  fork  (vibration  number}      .      

Temperature  of  air  of  room _____ 

Make  a  drawing  of  your  apparatus,  showing  the  position 
of  the  fork  arid  the  length  of  the  air  column  at  the  point 
of  maximum  resonance.  Write  a  simple  description  of 
how  the  experiment  was  done. 

The  measured  length  of  the  air  column  is  not  quite 
correct  for  the  distance  traveled  by  the  sound  in  one 
quarter  of  a  vibration.  It  actually  travels  a  little  farther, 
owing  to  the  reflection  from  the  sides  of  the  tube  and  the 
spreading  at  the  open  end.  Adding  0.4  of  the  diameter 
of  the  tube  to  the  length  makes  the  necessary  correction. 

CALCULATED  RESULTS 

i         n 

Correction  for  air  column  (0.4  d'am.) 
Corrected  length  of  air  column  .... 

(length  +  0.4  diameter) 
Wave  length  produced  by  fork  in  air  .     .     

(4  x  corrected  length) 


128  LABORATORY  EXERCISES 

Discussion : 

By  reference  to  a  lettered  diagram  showing  a  prong  of  the 
fork  and  an  air  column,  tell  why  four  times  the  length 
of  the  resonating  column  is  taken  as  the  wave  length  of 
the  fork. 

Conclusion : 

The  length  of  a  sound  wave  from  a  C  fork  (256  V.P.S.) 

at °  C.  was inches. 

(average) 

Velocity  of  Sound- — The  wave  length  of  sound  pro- 
duced by  a  fork  multiplied  by  the  number  of  its  vibra- 
tions per  second  (frequency)  gives  the  velocity  of  sound 
per  second. 

If  the  instructor  so  directs,  make  this  calculation,  using 
the  data  already  obtained.  Remember  to  divide  the 
product  by  12  in  order  to  express  the  velocity  of  sound  in 
feet  per  second  at  the  temperature  of  the  room. 


LAWS  OF  VIBRATING   STRINGS  129 

EXPERIMENT  36 

Laws  of  Vibrating  Strings 

OBJECT.  To  find  how  the  frequency  depends  upon  (a)  the  length 
when  the  tension  is  constant,  (&)  the  tension  when  the  length  is 
constant. 

APPARATUS.  A  simple  sonometer,  like  the  apparatus  used  in 
Experiment  7,  page  37,  modified  to  use  with  shorter  wire  and  a 
meter  stick;  bridge  for  sonometer  ;  steel  piano  wire,  about  26  B. 
&  S.  gauge  ;  slotted  weights  running  to  5  kg.  or  about  10  Ib. ; 
tuning  forks1  C  (256  V.P.S.),  A  (426|  V.P.S.),  and  C'  (512 
V.P.S.)  ;  flat  cork,  2". 

Introductory : 

No  form  of  music  is  more  appreciated  than  that  pro- 
duced by  stringed  instruments.  There  is  a  fascination  in 
watching  the  play  of  a  violinist's  fingers  as  he  changes 
the  lengths  of  the  vibrating  strings.  In  the  preliminary 
tuning  of  the  violin  the  strings  are  tightened  by  putting 
more  pull  or  tension  upon  them.  All  these  adjustments, 
made  so  readily  by  the  practiced  violinist,  are  in  accord- 
ance with  a  few  simple  laws  relating  to  vibrating  strings. 
These  laws  may  be  determined  in  the  laboratory  by  the 
use  of  simple  apparatus  and  a  little  patient  observation. 

Experimental : 

Arrange  the  apparatus  as  in  Fig.  51,  placing  the  bridge 
(B)  about  60  cm.  from  the  fixed  end  (J.).  Add  enough 
weight  to  stretch  the  wire  tight  so  that  the  wire  will  give 

a  clear  note  when  it  is  plucked. 

• 

1  A  G  fork  (frequency  384)  would  be  recommended  for  this  experiment 
in  preference  to  the  A  fork,  were  it  not  for  the  relative  cheapness  of  the 
latter. 


130 


LABORATORY  EXERCISES 


(a)  Law  of  Lengths. — Set  the  string  AB  vibrating 
by  plucking  it  with  your  first  finger.  Strike  a  C  tuning 
fork  (frequency  256)  on  a  flat  cork,  and  note  'whether  or 
not  the  fork  and  the  wire  give  sounds  of  the  same  pitch. 
This  unison  can  be  told  by  the  absence  of  beats.  If  the 
sounds  are  not  in  unison,  increase  the  tension  by  adding 
more  weight,  and  try  again.  Continue  in  this  manner 
until  unison  is  obtained,  shifting  the  bridge  a  little,  if 
necessary.  Then  the  string  and  the  fork  are  making  the 


£       IT                               1 

Fig.  51. 

same  number  of  vibrations  per  second.  Measure  and 
record  the  length  AB  of  the  string  which  gives  256  vi- 
brations per  second. 

With  the  tension  remaining  the  same,  adjust  the  length 
of  the  vibrating  string  so  that  it  is  in  unison  with  an  A 
fork  (frequency  426).  Do  this  by  moving  the  bridge. 
Measure  and  record  the  length  of  the  vibrating  wire.  Is 
this  wire  which  gives  426  vibrations  shorter  or  longer  than 
the  wire  with  the  frequency  of  256  ? 

Again  vary  the  length  of  the  vibrating  wire  so  as  to 
bring  it  into  unison  with  a  C'  fork  (frequency  512). 
Measure  and  record.  How  does  this  length  compare  with 


LAWS  OF  VIBRATING  STRINGS  131 

the  length  of  a  string  which  makes  half  as  many  vibra- 
tions per  second,  the  tension  remaining  the  same  ? 

(J)  Law  of  Tensions.  —  Record  the  weight  which  in 
Part  (a)  gave  the  tension  on  the  wire  with  a  frequency  of 
512.  Keeping  the  vibrating  wire  the  same  length,  grad- 
ually decrease  the  tension  by  removing  weight,  until  the 
wire  is  in  unison  with  the  C  fork  (frequency  256),  as 
nearly  as  the  weight  permits.  Record  the  tension. 

Find  the  ratio  of  the  square  roots  of  the  two  tensions. 
What  else  has  the  same  ratio  when  the  length  of  the  vi- 
brating string  is  kept  constant  ? 

If  there  is  time,  and  if  the  instructor  so  directs,  verify 
the  relation  just  formed  by  putting  such  a  tension  on  the 
wire  as  will  make  it  vibrate  in  unison  with  an  A  fork 
(approximate  frequency  426). 


OBSERVATIONS 
Part  (a):  Law  of  lengths  (tension  constant). 

FORK  FREQUENCY          LENOTU  OF  WIBE  IN  U* 

C  cm. 

A  cm. 

C'  cm. 

Part  (6):  Law  of  tensions  (length  constant}. 

FREQUENCY  or  WIKK  TENSION  (WEIGHT) 

512 
256 
426 


Make  -a  diagram  of  your  apparatus.     Describe  briefly 
the  method  in  each  part  of  the  experiment. 


132  LABORATORY  EXERCISES 

CALCULATED  RESULTS 
Part(b*): 

FREQUENCY  OF  WIRE  SQUARE  ROOT  OF  TENBIOS* 

512 
256 
426 

Discussion : 

What  is  the  quickest  way  of  raising  the  pitch  (fre- 
quency) of  a  violin  string  ?  What  is  the  effect  of  tight- 
ening a  violin  string  ?  Explain. 

Conclusion : 

State  (a)  the  relation  of  pitch  (frequency  of  vibration) 
to  the  length  of  a  vibrating  string  when  the  tension  is 
constant;  (6)  the  relation  of  pitch  to  the  square  root  of 
the  tension  when  the  length  is  constant. 


MEASUREMENT  OP  CANDLE  POWER  133 

EXPERIMENT  37 

Measurement  of  Candle  Power 

OBJECT.  To  determine  the  candle  power  of  a  lamp  by  means  of 
a  Jolly  or  a  Bunsen  photometer. 

APPARATUS.  A  Jolly1  or  a  Bunsen  photometer;  2  incandes- 
cent lamps,  one  of  known  candle  power.  If  electricity  is  not 
available,  a  standard  candle  and  an  oil  lamp  may  be  used.  The 
ordinary  paraffin  candle,  "  6's  "  or  "  12's,"  are  about  1.25  candle 
power. 

Introductory: 

The  ordinary  incandescent  lamp  is  rated  at  16  candle 
power.  This  means  that  it  gives  16  times  as  much  light 
as  one  standard  candle.  If  the  candle  is  placed  on  one 
side  of  a  translucent  screen  and  the  lamp  on  the  other,  the 
screen  can  be  moved  to  a  position  where  it  is  equally  illu- 
minated on  both  sides.  The  screen  receives  the  same 
intensity  of  illumination  from  both  lights,  but  the  greater 
candle  power  of  the  lamp  permits  it  to  be  much  farther 
from  the  screen  than  the  candle.  If  the  latter  is  20  cm. 
from  the  screen,  then  the  distance  of  the  lamp  will  be 
found  to  be  80  cm.  It  is  interesting  to  note  that  the 

1  The  Jolly  photometer  consists  of  two  slices  of  paraffin  about  5  cm. 
square,  cut  from  blocks  of  "  Para  wax,"  and  of  equal  thickness,  separated 
by  a  sheet  of  tin  foil  (Fig.  62).  These  disks  are  mounted  at  the  center  of 
a  block  about  18  cm.  long  and  held  in  place  by  a  rectangular  hood  of 
tin  (T)  nailed  to  the  block  (W)  (Fig.  63).  The  junction  of  the  two 
blocks  is  viewed  through  an  opening  in  the  tin  hood,  at  the  center  of  the 
screen.  The  block  and  hood  should  be  painted  black.  The  different 
photometers  in  the  laboratory  should  be  so  placed  that  each  screen  re- 
ceives light  from  its  own  lamps  only. 

The  authors  are  indebted  to  Mr.  W.  R.  Pyle  of  the  Morris  High 
School,  New  York,  for  the  simple  method  of  mounting  the  Jolly  screen 
given  above. 


134  LABORATORY  EXERCISES 

squares  of  these  distances  from  the  screen  have  the  same 
ratio  as  the  relative  candle  power  of  the  two  lights : 

ILLUMINATING  POWER    ILLUMINATING  POWEK      SQUARE  OF  CANDLE     SQUARE  OF  LAMP 
OF  CANDLE  OF  LAMP  DISTANCE  FROM         DISTANCE  FROM 

SCREEN  SCREEN 

1  :  16  ::          400          :       6400 

Hence  the  ratio  of  the  illuminating  power  of  two  lights 
equals  the  ratio  of  the  squares  of  their  respective  distances 
from  the  equally  illuminated  screen. 

The  screen  device  for  determining  relative  candle  power 
is  known  as  a  photometer.  Owing  to  the  difficulty  of 
getting  candles  of  exact  candle  power,  the  candle  power 
of  lamps  in  commercial  practice  is  usually  found  by  com- 
parison with  standard  incandescent  lamps,  whose  candle 
power  has  been  accurately  determined. 

Experimental : 

If  the  photometer  differs  from  that  shown  in  Fig.  52,  the 
instructor  will  give  directions  for  its  use.  In  the  Jolly 
photometer  (Fig.  52),  two  slices  of  paraffin,  separated  by 


Fig.  52. 

a  sheet  of  tin  foil,  are  used  for  the  translucent  screen. 

The  tin  foil  prevents  the  light  received  from  one  lamp 
from  illuminating  the  other  side  of  the  screen. 
The  light  is  reflected  instead,  and  intensifies  the 
illumination  in  the  half  of  the  paraffin  facing  the 
lamp.  When  the  two  halves  of  the  screen  are 
equally  illuminated,  the  two  halves  of  the  exposed 

Fig.  53.     ends  will  have  the  same  shade. 


MEASUREMENT  OF  CANDLE  POWER  135 

Start  with  an  incandescent  lamp  of  known  candle  power, 
and  compare  with  it  a  lamp  of  unknown  candle  power,  as 
follows: 

(1)  Place    the    incandescent  lamp   of    known   candle 
power   in    one    socket   and    the    unknown    lamp   in    the 
other.     Both  sockets  should   be  connected  to  the  same 
current  outlet. 

(2)  Slide  the  screen  along  the  meter  stick,  until  the 
two  halves  of  the  paraffin  are  of  the  same  shade  of  bright- 
ness.    Record  in  tabular  form,  near  the  top  of  the  left- 
hand  page,  the  position  on  the  meter  stick  of  the  standard 
lamp,  that  of  the  unknown  lamp,  and  that  of  the  screen. 

(3)  Move  the  lamp  away  from  its  position  and  make  a 
second  independent  setting.     The  average  of  each  pair  of 
distances  obtained  should  be  used  in  making  the  final  cal- 
culation. 

OBSERVATIONS 

NUMBER  OF  POSITION  OF  POSITION  OF          POSITION  OF  CANDLE  POWER 

READING  STANDARD  UNKNOWN  SCREEN  OF  STANDARD 


1 

2 

Make  a  drawing,  showing  the  essential  parts  of  the  pho- 
tometer, and  describe  how  you  used  it. 

Using  the  ratio  method  given  in  the  "  Introductory,"  cal- 
culate the  candle  power  of  the  unknown  lamp,  placing  the 
calculated  results  at  the  top  of  the  right-hand  page. 


CALCULATED  RESULTS 

AVERAGE  DISTANCE  /STAND 

OF  STANDARD  OF  UNKNOWN  \DISTANCB  )          VDISTANCB 


AVERAGE  DISTANCE  AVERAGE  DISTANCE  />r  v\i>ARD\2        /UNKifowN\2 

OF  UNKNOWN  \DISTANCK  /  \DISTANCE  / 


Candle  power  determined  for  unknown.. 


136  LABORATORY  EXERCISES 

Discussion : 

Demonstrate  the  relation  between  the  distance  and  the 
intensity  of  illumination. 

How  would  you  determine  the  candle  power  of  a 
lantern  ? 

Conclusion : 

The  candle  power  of  lamp  No. is . 


EXPERIMENT  37   (Alternative) 

Measurement  of  Candle  Power 

OBJECT.  To  determine  the  candle  power  of  a  lamp  by  means 
of  the  Rumford  photometer. 

APPARATUS.  Ring  stand ;  vertical  screen ;  meter  stick ; 
2  incandescent  lamps,  one  of  known  candle  power.  If  electricity 
is  not  available,  a  standard  candle  and  an  oil  lamp  may  be  used. 
The  ordinary  paraffine  candle  "  6's  "  or  "  12's"are  about  1.25 
candle  power.  A  small  lantern  is  a  very  desirable  form  of  the  oil 
lamp  for  this  experiment  on  account  of  its  candle  power  and 
its  safety  for  laboratory  use. 

Introductory: 

A  16  candle  power  lamp  is  one  which  gives  16  times  as 
much  light  as  one  standard  candle.  If  a  candle  and  a 
lamp  are  both  placed  on  the  same  side  of  a  rod,  they  will 
each  cast  a  shadow  of  the  rod  on  a  screen  placed  behind 
it.  Each  will  then  illuminate  the  shadow  cast  by  the 
other.  If  the  shadows  are  equally  dark,  then  the  screen 
receives  the  same  intensity  of  illumination  from  both 
lights.  The  greater  candle  power  of  the  incandescent 


MEASUREMENT  OF  CANDLE  POWER  137 

lamp,  however,  permits  it  to  be  much  farther  from  the 
screen  than  the  candle.  If  the  latter  is  20  m.  from  the 
screen,  then  the  distance  of  the  lamp  will  be  found  to 
be  80  m. 

It  is  interesting  to  note  that  the  square  of  these  dis- 
tances from  the  screen  have  the  same  ratio  as  the  rela- 
tive candle  power  of  the  two  lights  : 

ILLUMINATING          ILLUMINATING         SQUARE  OF  CANDLE  SQUARE  OF  LAMP 

POWKB  OF  CANDLB    POWKB  OF  LAMP    DISTANCE  FEOM  SCREEN    DISTANCE  FROM  SCUEKN 

1  :         16         ::  400  :          6400 

Hence  the  ratio  of  the  illuminating  power  of  the  two  lights 
equals  the  ratio  of  the  squares  of  their  respective  distances 
from  the  equally  illuminated  screen. 

The  photometer  which  determines  candle  power  by 
means  of  shadows  cast  upon  an  opaque  screen  is  the  Rum- 
ford  photometer. 

Experimental : 

1.  Place  the  upright  rod  of  the  ring  stand  about  10  cm. 
from  the  vertical  screen. 

2.  Place  the  lamp  whose  candle  power  is  to  be  deter- 
mined at  a  distance  of  about  120  cm.  from  the  screen. 

3.  Place  the  standard  lamp  (or  candle)  in  such  a  posi- 
tion that  the  two  shadows  of  the  rod  formed  on  the  screen 
shall  be  of  the  same  intensity.     These  shadows  should  be 
near  each  other,  but  should  not  overlap. 

Measure  with  the  meter  stick  the  distance  of  the  stand- 
ard lamp  to  the  nearer  of  the  two  shadows,  and  the  dis- 
tance from  the  unknown  lamp  to  the  other  shadow. 
Record  the  results  in  tabular  form  near  the  top  of  the 
left-hand  page.  Why  was  the  distance  measured  in  each 
case  to  the  nearer  of  the  two  shadows  ? 


138 


LABORATORY  EXERCISES 


4.  Repeat  the  above  test  with  the  unknown  lamp  (or 
candle)  successively  at  100  cm.  and  80  cm.  from  the 
screen. 

In  case  two  incandescent  lamps  are  compared,  their 
sockets  should  be  connected  to  the  same  current  outlet. 

OBSERVATIONS 


NUMBER  OF 
TRIAL 

DISTANCE  OF  UNKNOWN 
FBOM  SCREEN 

DISTANCE  OF  STANDARD 
FROM  SCREEN 

1 

cm. 

cm. 

2 

cm. 

cm. 

3 

cm. 

cm. 

Candle  power  of  standard . 

Make  a  drawing  showing  the  essential  parts  of  the 
photometer,  and  describe  how  you  used  it. 

Using  the  ratio  method  given  in  the  "  Introductory," 
calculate  the  candle  power  of  the  unknown  lamp,  placing 
the  calculated  results  in  tabular  form  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 


NUMBER  OF 
TRIAL 

/STANDARD  \' 
V  DISTANCE  / 

/UNKNOWN\' 
V  DISTANCE  / 

CANDLE  POWER 
OF  UNKNOWN 

1 

2 

3 

Average 

'         



Discussion : 

Demonstrate  the  relation  between  the  distance  and  the 
intensity  of  illumination. 


LAW  OF  REFLECTION  OF  LIGHT  139 


Conclusion : 

The  candle  power  of is 

(name  lamp) 


EXPERIMENT    38 

Law  of  Reflection  of  Light 

OBJECT.  To  determine  the  relation  between  the  angle  of  in- 
cidence and  the  angle  of  reflection. 

APPARATUS.  Glass  or  metal  mirror ;  clamp  or  block  for 
holding  mirror  ;  sheet  of  clear  glass  the  same  size  as  the  mirror ; 
pins  ;  ruler ;  protractor. 

Introductory : 

When  sunlight  falls  upon  a  mirror,  the  light  is  reflected 
in  a  definite  direction.  The  relation  between  the  direction 
of  the  light  before  and  after  it  strikes  the  mirror  is  stated 
in  the  law  of  reflection.  We  can  locate  a  particular  re- 
flected ray  by  sighting  along  a  ruler  at  the  image  of  the 
object  that  is  reflected.  A  line  drawn  along  the  edge  of 
the  ruler  will  mark  the  direction  of  the  reflected  ray. 

Experimental : 

(1)  Draw  a  line  across  the  middle  of  the  right-hand 
page  of  your  note-book.     Mark  it  MM.     Place  the  mirror 
perpendicular  to  the  page  with  its  reflecting  surface  on 
this  line.     Stick  a  pin  upright  in  the  page  in  front  of  the 
mirror  and  mark  its  position  P. 

(2)  Placing  the  head  on  the   level   of  the   page  and 
opposite  one  of  the  lower  corners  of  the  book,  sight  along 
a  ruler  placed  on  the  page  at  the  image  of  the  pin,  as  seen 
in  the  mirror.     When  the  edge  of  the  ruler  is  exactly  in 


140 


LABORATORY  EXERCISES 


a  line  with  the  image  of  the  pin,  draw  a  line  along  the 
edge  of  the  ruler. 

(3)  Repeat  the  operations  described  in  (2),  with  the 
eye  near  the  other  lower  corner  of  the  book. 


Fig.  54. 


(4)  Remove   the  mirror  and  substitute  a   transparent 
sheet  of  glass,  carefully  placing  its  front  edge  on  the  line 
MM.     Protect  the  page  behind  the  mirror  from  the  direct 
light  of  the  windows.     Looking  through  this  transparent 
mirror,  insert  a  pin  to  coincide  with   the   image  of   P. 
Mark   the  position  of  this  pin  P'.     Remove   the  mirror 
and  pins. 

(5)  Continue  each  of  the  lines  drawn  along  the  edge  of 
the  ruler  as  solid  lines  to  the  mirror  line  MM,  and  con- 
tinue them  as  dotted  lines  behind  the  mirror  until  they 
meet.     Do  these  solid  lines  represent  incident  or  reflected 
rays  f 

From  P  draw  a  line  to  the  intersection  of  each  of  the 
lines  just  drawn  with  the  mirror  line.     Do  these  lines  from 


LAW  OF  REFLECTION  OF  LIGHT  141 

P  mark  incident  or  reflected  rays  ?  Connect  P  and  P' 
with  a  line,  solid  from  P  to  the  mirror  and  dotted  from 
the  mirror  to  P' .  Mark  the  direction  in  which  light  is 
passing  along  each  of  the  solid  lines  by  an  arrow  on  that  line. 

(6)  At  the  intersection  of  one  of  the  solid  lines  with 
the  mirror  line,  erect  a  perpendicular  to  the  mirror  line. 
The  angle  between  the  line  coming  from  the  pin  to  the 
mirror  and  this  perpendicular  line  is  called  the  angle  of 
incidence.  The  angle  between  the  reflected  ray  and  this 
perpendicular  is  called  the  angle  of  reflection.  Measure 
these  angles  with  a  protractor. 

Record  in  tabular  form  near  the  top  of  the  left-hand 
page  the  measurements  called  for. 

OBSERVATIONS 

Angle  of  incidence 

Angle  of  reflection , 

Distance  of  pin  from  mirror cm. 

Distance  of  image  from  mirror cm. 

Angle  between  MM  and  PP' 

A  simple  sketch  of  the  apparatus  as  seen  from  above 
should  be  made  and  the  experimental  operations  described 
briefly. 

Discussion : 

Answer  the  italicized  questions  occurring  in  the  ex- 
perimental directions.  As  seen  in  the  mirror,  from  what 
point  do  the  rays  sighted  along  the  ruler  appear  to  come  ? 
From  what  point  do  they  actually  come  ? 

Compare  the  distance  of  the  image  of  the  pin  as  seen 
in  the  mirror  with  the  distance  of  the  pin  itself. 

Conclusion : 

State  the  relation  between  the  angle  of  incidence  and 
the  angle  of  reflection. 


142  LABORATORY  EXERCISES 

EXPERIMENT    39 

Images  in  a  Plane  Mirror 

OBJECT.  To  compare  an  object  with  its  image  in  a  plane  mirror 
with  respect  to  size,  distance,  and  form. 

APPARATUS.  Glass  plate  for  mirror ;  wooden  block  with  slot 
for  holding  mirror  in  vertical  position ;  half-meter  stick,  or  foot 
ruler ;  pins. 

Introductory : 

The  plane  mirrors  which  hang  on  our  walls  give  rise  to 
some  interesting  questions.  Why  does  your  image  in 
the  mirror  seem  to  approach  you  as  you  walk  toward  the 
mirror  ?  Why  do  you  sometimes  move  your  hand  in  the 
wrong  direction  when  attempting  to  adjust  something  on 
your  head  ?  Why  is  a  long  mirror  desirable  when  you 
want  to  see  your  apparel  from  head  to  foot  ?  An  answer 
to  these  questions  will  be  found  in  the  study  of  the 
relations  of  the  object  to  the  image  in  a  plane  mirror. 

The  image  of  an  object  is  composed  of  the  images  of  the 
points  in  that  object.  We  can  locate  the  image  of  each 
point  in  a  transparent  mirror  by  direct  observation,  as 
was  shown  in  the  experiment  on  the  law  of  reflection. 

Experimental : 

Draw  a  line  across  the  middle  of  the  right-hand  page  of 
your  note-book.  About  two  inches  below  this  line  of 
reference  make  a  drawing  of  a  quadrilateral  set  obliquely 
to  the  line,  no  side  of  the  drawing  to  be  less  than  1^  inches 
in  length.  Number  the  corners  1,  2,  3,  and  4,  as  in 
Fig.  55. 

Place  the  front  of  the  glass  plate  along  the  line  of 
reference.  Place  a  pin  at  point  1  of  your  drawing  and 


IMAGES  IN  A  PLANE  MIRROR  143 

set  a  second  pin  at  the  image  of  1  as  seen  in  the  mirror. 
Mark  the  position  of  the  image  pin  with  a  pencil  dot  and 
the  figure  1'.     Locate  and  mark  the  image  of  each  corner 
in  the  same  way.     Connect  these 
points  by  lines  representing  the 
images    of    the     corresponding 
edges  of  the  block. 

Shading  the  part  of  the  note- 
book behind  the  mirror  helps 
to  secure  a  clear  image  in  the  Fig-  5S- 

mirror. 

Compare  the  object  and  the  image  by  means  of  the 
following  measurements,  which  should  be  recorded  in 
tabular  form  near  the  top  of  the  left-hand  page. 

OBSERVATIONS 

LINES  8-4     LINES  1-3 

Length  of  lines  in  object 

Length  of  lines  in  image     .     ,.     .     .     .        

POINTS          1  284 

Distance  of  object"1*  points 
from  mirror     ....     

POINTS         1'  2'  8'  4' 

Distance  of  image's  points 
from  mirror     ....     

Write  a  brief  description  of  the  method  of  the  experi- 
ment on  the  left-hand  page. 

Conclusion: 

( )n  the  second  right-hand  page,  answer  the  following 
questions,  using  a  complete  sentence  for  each  answer. 

1.  What   relation  exists  between   the   object  distance 
and  the  image  distance  of  a  point  from  the  mirror  line  ? 

2.  Compare  the  size  of  the  object  and  its  image. 


144  LABORATORY  EXERCISES 

3.  Is  the  image  formed  by  a  vertical  mirror  erect  or 
inverted  ?     (Before  answering,  consider  your  own  image 
in  a  mirror.)     Is  the  image  of  the  pin  in  front  of  the 
mirror  or  behind  it  ? 

4.  In  which  direction  do  the  hands  of  a  watch  appear  to 
turn  when  viewed  in  a  mirror  ? 

5.  Are  an  object  and  its  image  in  a  plane  mirror  similar 
or  symmetrical  ? 

EXPERIMENT   40 

Reflection  in  a  Concave  Mirror 

OBJECT.  To  study  the  form  and  location  of  the  images  formed 
by  a  concave  mirror. 

APPARATUS.  Concave  spherical  mirror  of  glass  or  metal,  sup- 
ported in  a  vertical  position ;  two  meter  sticks  so  placed  as  to 
form  a  V  with  its  apex  beneath  the  center  of  the  mirror ;  two 
screens  mounted  so  as  to  slide  on  the  meter  sticks  —  one  screen 
is  opaque  and  the  other  has  cut  in  it  a  round  or  square  window, 
over  which  is  pasted  very  thin  paper,  with  ink  lines  ruled  across 
it  at  right  angles  and  an  ink  mark  in  one  of  the  four  spaces  formed 
by  the  intersecting  lines ;  candle  or  incandescent  lamp,  to  be 
placed  behind  the  translucent  window. 

Introductory : 

The  beam  of  light  from  a  headlight,  where  the  burner  is 
quite  near  the  surface  of  a  concave  reflector,  is  shaped  like 
a  cone  with  its  apex  behind  the  reflector.  The  beam  from 
a  searchlight  may  take  a  conical  shape  like  that  from  the  re- 
flector. It  may,  however,  be  made  parallel,  or  it  may  even 
be  brought  to  a  brilliant  focus  at  some  point  in  front  of  the 
searchlight.  These  changes  in  the  shape  of  the  beam  are 
possible  because  the  distance  between  the  light  and  its 


REFLECTION  IN  A  CONCAVE  MIRROR 


145 


concave  reflector  can  be  varied.  The  position  of  the  light 
when  the  reflected  rays  are  parallel  is  called  the  principal 
focus  and  the  perpendicular  distance  from  the  principal 
focus  to  the  mirror  is  the  focal  length  of  the  mirror.  For 
every  case  of  reflection  from  a  concave  mirror  a  definite 
relation  exists  between  the  distance  of  the  object,  the  dis- 
tance of  its  reflected  image,  and  the  focal  length  of  the 
mirror. 

Experimental : 

(a)  In  a  darkened  room,  the  translucent  screen,  lighted 
from  behind,  is  placed  on  one  of  the  meter  sticks  at  a  con- 
siderable distance  from  the  mirror.  The  opaque  screen, 
on  the  other  meter  stick,  is  then  moved  backward  and  for- 
ward until  a  position  is  found  where  the  most  distinct  image 


Fig.  56. 

of  the  lighted  window  is  formed.  Record  the  distance  of 
each  screen  from  the  mirror,  also  whether  the  image  is 
larger  or  smaller  than  the  object  and  whether  the  image  is 
erect  or  inverted.  Note  in  this  and  in  each  of  the  follow- 
ing cases  whether  there  is  any  image  back  of  the  mirror, 
as  in  the  case  of  the  plane  mirror. 

(i)  Find  another  pair  of  positions  for  the  screens  where 
the  image  will  now  be  larger  than  the  object,  if  it  was 
smaller  before,  or  vice  versa.  The  same  items  are  to  be 
recorded  as  before. 


146 


LABORATORY  EXERCISES 


(V)  Another  pair  of  positions  is  to  be  found  where  the 
image  will  be  as  nearly  as  possible  the  same  size  as  the 
object,  and  a  similar  record  made. 

(<2)  The  lighted  window  is  next,  moved  toward  the 
mirror,  until  there  is  no  image  formed  on  the  opaque 
screen  at  any  distance,  but  an  image  appears  to  be  formed 
behind  the  mirror.  The  position  of  the  lighted  screen 
and  the  general  location  and  character  of  the  image  are  to 
be  recorded. 

(V)  Finally  the  illuminated  screen  is  removed,  and  the 
meter  stick  on  which  this  screen  rests  is  pointed  through 
the  window  at  some  distant  object  outside.  If  the  weather 
permits,  the  window  should  be  open.  The  location  of  the 
image  should  be  recorded.  This  image  is  at  the  principal 
focus  of  the  mirror. 

All  observations  should  be  recorded  in  a  table  near  the 
top  of  the  left-hand  page.  Where  distances  are  not  meas- 
ured, record  general  position  of  object  or  image. 


OBSERVATIONS 


TRIAL 

OBJECT  DISTANCE 

IMAGE  DISTANCE 

IMAGE  EKECT  OB 
INVERTED 

IMAGE  ENLARGED 
OR  DIMINISHED 

a 

cm. 

cm. 

b 

cm. 

cm. 

c 

cm. 

cm. 

d 

cm. 

cm. 

e 

cm. 

cm. 

Make  a  simple  outline  drawing  of  your  apparatus.  A 
view  from  above,  showing  the  location  of  the  mirror, 
screens,  and  meter  sticks,  will  be  sufficient.  Describe 
briefly  your  observations,  stating  particularly  anything 


REFLECTION   IN  A  CONCAVE   MIRROR 


147 


you  observe  about  the  images  which  is  not  recorded  in  the 
table  above. 

For  cases  («),  (6),  and  (<?),  calculate,  as  decimals,  the  re- 
ciprocals of  the  object  distance  and  of  the  image  distance. 

From  (e)  calculate  the  reciprocal  of  the  principal  focal 
length.  This  is  to  be  compared  in  each  case  with  the 
sum  of  the  other  two  reciprocals.  All  results  are  to  be 
recorded  in  tabular  form  at  the  top  of  the  right-hand  page. 


CALCULATED  RESULTS 


TBIAL 

, 

1 

1              ,             1 

1 

OBJECT  DIST. 

IMAGE  DIST. 

OBJECT  DIST.      IMAGE  DIST. 

FOCAL  LENGTH 

a 

b 

c 

Discussion : 

(1)  When  an  object  is  at  the  center  of  curvature  of  a 
concave  mirror  (that  is,  at  the  center  of  the  sphere  from 
which  the  mirror  is  cut),  the  image  is  at  the  same  place 
and  of  the  same  size  as  the  object.     Do  any  of  your  read- 
ings give  you  the  radius  of  the  curvature  of  your  mirror? 
If  so,  which  trial  ? 

(2)  When  the  object  is  at  a  distance  greater  than  the 
radius  of  curvature,  describe  the  image  as  to  whether  it  is 
real  or  virtual,  erect  or  inverted,  enlarged  or  diminished. 
State  the  location  of  the  image  with  reference  to  the  center 
of  curvature  and  to  the  principal  focus. 

(3)  "  When  the  object  is  between  the  center  of  curvature 
and  the  principal  focus,  the  image  is  ..."     (Complete 
the  statement,  touching  on  each  of  the  points  noted  in  (2).) 

(4)  "  When  the  object  is  between  the  principal  focus 


148  LABORATORY  EXERCISES 

and  the  mirror,  the  image  is  ..."     (Complete  as  in  (2) 
and  (3).) 

(5)  What  kind  of  rays  are  reflected  to  the  principal 
focus?  Where  must  an  object  be  to  send  rays  of  approxi- 
mately this  character  ? 

Conclusion : 

What  is  the  relation  between  the  reciprocal  of  the  focal 
length  of  a  concave  mirror  and  the  sum  of  the  reciprocals 
of  the  object  distance  and  the  image  distance  ?  Give  your 
answer  both  in  words  and  in  an  algebraic  form. 


EXPERIMENT   41 

Reflection  in  a  Convex  Mirror 

OBJECT.  To  study  the  form  and  location  of  the  images  formed 
by  a  convex  mirror. 

APPARATUS.  Convex  spherical  mirror,  mounted  in  a  vertical 
position ;  candle  or  incandescent  lamp ;  meter  stick,  with  sliding 
opaque  screen  mounted  on  it. 

Introductory : 

A  polished  door  knob  reflects  a  distorted  image  of  the 
objects  in  the  room.  Other  bulging  curved  surfaces  re- 
flect in  a  similar  manner.  Convex  spherical  mirrors  are 
frequently  used  as  pocket  mirrors. 

Experimental : 

Place  the  candle  or  lamp  in  a  considerable  number  of 
positions,  at  different  distances  from  the  mirror.  At  each 
position,  observe  the  character  and  location  of  the  image 


REFRACTION  THROUGH  A  GLASS  PLATE        149 

formed.     As  the   object   approaches   the   mirror,   notice 
whether  the  image  approaches  or  recedes. 

Make  a  simple  sketch  of  the  apparatus  and  give  a  brief 
description  of  your  work;  a  tabulation  of  observations  and 
results  is  not  necessary,  as  these  are  to  be  summed  up  in 
the  Conclusion. 

Conclusion  : 

Make  a  general  statement  as  to  the  character  (real  or 
virtual),  position  (erect  or  inverted),  shape  (similar  to 
object  or  symmetrical  with  it),  and  location  of  the  images 
formed  by  a  convex  mirror. 


EXPERIMENT  42 

Refraction  through  a  Glass  Plate1 

OBJECT.  To  study  the  refraction  of  a  ray  of  light  through  a 
thick,  rectangular  glass  plate. 

APPARATUS.     Thick  rectangular  glass  plate ;  ruler ;  pins. 

Introductory : 

When  we  look  through  a  thick  plate  of  glass,  objects 
seem  displaced  to  one  side  or  the  other.  This  is  the  effect 
of  refraction.  We  may  study  this  effect  by  marking  the 
path  of  an  oblique  ray  with  two  pins  before  it  enters  the 
plate,  and  then  sight  along  a  ruler  to  determine  the  emer- 
gent ray. 

1  Note  to  Instructor.  If  a  qualitative  treatment  of  refraction  is  desired, 
students  should  perform  Experiment  42  or  Experiment  43,  or  both.  The 
quantitative  treatment,  as  well  as  the  qualitative,  is  provided  for  in  Ex- 
periment 44. 


150 


LABORATORY  EXERCISES 


Experimental : 

Place  a  rectangular  plate  of  glass  near  the  center  of  the 
right-hand  page  of  your  note-book,  having  two  clear  edges 
parallel  to  the  top  and  bottom  of  the  book.  With  a 
sharp,  hard  pencil,  trace  the  outline  of  the  plate  of  glass 
on  the  page. 

Near  a  corner  of  the  upper  edge,  draw  a  line  at  an  angle 
to  the  upper  edge  of  the  glass.  On  this  line  place  two 

pins,  several  centimeters 
apart.  Place  the  eye  on  a 
level  with  the  glass  plate. 
Looking  through  the  glass, 
place  a  ruler  between  the 
block  and  your  eye,  so 
that  you  can  sight  along 
its  edge  at  the  other  two 
pins,  as  seen  through  the 
glass.  Trace  the  position 
of  the  edge  of  the  ruler. 

Remove  the  glass  and 
pins.  Continue  the  lines 
you  have  drawn  until  they 

have  met  the  lines  indicating  the  surfaces  of  the  plate. 
Draw  a  line  representing  the  path  of  the  light  through 
the  glass,  indicating  by  arrowheads  on  all  lines,  the 
direction  in  which  the  light  is  proceeding. 

On  the  diagram,  at  the  point  where  the  ray  of  light 
entered  the  glass,  draw  a  dotted  line  perpendicular  to  the 
surface  of  the  plate,  and  continue  it  part  way  across  the 
rectangle  representing  the  plate. 

At  the  point  where  the  light  ray  emerged,  draw  a  similar 
dotted  perpendicular  and  continue  it  upward  into  the 
rectangle.  These  perpendiculars,  drawn  where  the  light 


Fig.  57. 


REFRACTION   THROUGH  A  PRISM  151 

ray  enters  or    emerges  from    the   plate,   are   known   as 
normals. 

Write  a  brief  description  of  the  method  of  the  experi- 
ment, referring  to  the  diagram.  No  other  drawing  is 
necessary. 

Conclusion : 

Make  a  general  statement  regarding  the  relative  di- 
rection of  the  entering  and  emerging  rays,  when  the  faces 
at  which  the  light  enters  and  emerges  from  the  medium 
are  parallel. 

A  ray  of  light  on  passing  from  a  rarer  to  a  denser 

medium  is  bent the  normal ;  in  passing  from  a  denser 

to  a  rarer  medium,  the  ray  is  bent the  normal. 


EXPERIMENT   43 

Refraction  through  a  Prism 

OBJECT.  To  study  the  refraction  of  a  ray  of  light  passing 
through  a  triangular  glass  prism. 

APPARATUS.  Triangular  glass  prism,  about  7  cm.  on  a  side 
and  1  cm.  thick;  ruler;  pins. 

Introductory  : 

Glass  prisms  at  one  time  were  hung  as  ornaments  in 
front  of  windows.  Objects  outside,  when  viewed  through 
a  prism,  seem  displaced  to  one  side  or  the  other.  This  is 
the  effect  of  refraction.  We  may  study  the  effect  of 
refraction  by  marking  the  path  of  an  oblique  ray  with 
two  pins  before  it  enters  the  prism,  and  then,  sighting 
along  a  ruler,  determine  the  emergent  ray. 


152  LABORATORY  EXERCISES 

Experimental : 

Place  a  triangular  glass  prism  near  the  center  of  the 
right-hand  page  of  your  note-book,  having  one  edge  of  the 
prism  parallel  to  the  bottom  of  the  page.  Trace  the  out- 
line of  the  prism  on  the  page  with  a  sharp,  hard  lead  pencil. 

A  little  to  the  right  of  the  center  of  the  left  edge  of  the 
prism  draw  a  line  at  an  angle  to  the  edge.  Do  not  make 
the  angle  between  the  ray  and  the  edge  more  than  45°,  or 
total  reflection  may  occur.  On  the  line  just  drawn,  place 
two  pins  several  centimeters  apart. 

Place  the  eye  on  a  level  with  the  glass  prism.  Looking 
through  the  glass,  place  a  ruler  between  the  prism  and 
your  eye,  so  that  you  can  sight  along  its  edge  at  the  two 
pins  as  seen  through  the  right  side  of  the  glass.  The 
ruler  should  be  moved  until  the  two  pins,  as  seen  through 
the  glass,  appear  in  the  same  straight  line.  Trace  the 
position  of  the  edge  of  the  ruler  on  the  page. 

Remove  the  glass  and  the  pins.  Continue  the  lines  you 
have  drawn  to  the  lines  representing  the  right-hand  edge 
and  the  left-hand  edge  of  the  prism  respectively.  Draw 
a  line  representing  the  path  of  the  light  through  the  glass, 
indicating  by  arrow-heads  on  all  lines  the  direction  in 
which  the  light  is  proceeding. 

On  the  diagram,  at  the  point  where  the  light  entered 
the  glass,  erect  a  dotted  line  perpendicular  to  the  surface 
of  the  glass,  and  continue  it  part  way  across  the  triangle 
representing  the  prism. 

At  the  point  where  the  light  emerged,  draw  a  similar 
dotted  perpendicular,  and  continue  it  into  the  triangle. 

These  perpendiculars  drawn  where  the  light  ray  enters 
or  emerges  from  the  prism  are  called  normals.  Note  the 
direction  of  bending  of  the  light  with  reference  to  the 
normals  at  each  surface  of  the  glass. 


INDEX  OF  REFRACTION  153 

A  brief  description  of  the  method  of  tracing  the  ray 
through  the  glass  should  be  written,  but  no  drawing  other 
than  the  diagram  is  necessary. 

Discussion : 

How  is  a  ray  of  light  bent  with  regard  to  the  normal : 
(a)  on  entering  a  denser  medium  ?  (6)  on  emerging  into 
a  rarer  medium  ? 

Conclusion : 

Is  light  bent  by  a  triangular  prism  toward  the  apex 
(refracting  angle)  or  toward  the  base  of  the  prism? 


EXPERIMENT   44 

Index  of  Refraction 
OBJECT.    To  determine  the  index  of  refraction  of  glass. 

APPARATUS.  Thick  rectangular  glass  plate,  or  triangular  glass 
prism  (1  cm.  thick)  or  both ;  pins ;  metric  ruler. 

Introductory : 

When  viewed  through  a  thick  plate  of  glass,  objects 
seem  displaced  to  one  side  or  the  other.  This  is  the  effect 
of  refraction.  This  effect  may  be  studied  by  marking 
the  path  of  an  oblique  ray  with  two  pins  before  it  enters 
the  plate,  and  then  sighting  along  a  ruler  to  determine  the 
emergent  ray. 

Light  travels  faster  in  air  than  in  a  denser  medium  like 
glass.  The  ratio  of  the  velocity  of  light  in  air  to  the 
velocity  of  light  in  glass  is  termed  the  index  of  refraction 
of  air  to  glass.  This  ratio  is  mathematically  equal  to  the 
ratio  of  the  sine  of  the  angle  of  incidence  (air  to  glass) 


154 


LABORATORY   EXERCISES 


to  the  sine  of  the  angle  of  refraction.  In  this  experi- 
ment you  will  learn  what  is  meant  by  the  angle  of 
incidence  and  the  angle  of  refraction.  You  will  con- 
struct and  measure  the  sine  of  each  of  these  angles. 
You  can  then  calculate  the  index  of  refraction  of  glass, 
relative  to  air. 

Experimental : 

If  a  rectangular  glass  plate  is  used,  follow  the  experi- 
mental directions  given  in  Experiment  42,  page  150. 
For  a  triangular  prism,  follow  Experiment  43,  page  152. 
Then  complete  the  experiment  according  to  the  directions 
which  follow. 

At  the  point  where  the  light  ray  enters  and  the  point 
where  it  emerges  from  the  glass,  perpendiculars  to  the  glass 
surface  (normals)  have  been  erected.  Indicate  the  angles 
between  the  incident  rays  and  the 
normals  as  angles  of  incidence;  those 
between  the  refracted  rays  and  the 
normals  as  angles  of  refraction. 
Taking  each  intersection  of  a  normal 
with  the  surface  of  the  glass  as  a  cen- 
ter, describe  circles  of  as  large  radius 
as  possible,  without  the  circles  inter- 
secting. From  the  intersection  of 
each  ray  with  its  circle,  drop  a  per- 
pendicular to  the  normal  in  that 
circle.  This  perpendicular  is  known 
as  the  sine  of  the  angle  of  incidence 
or  of  the  angle  of  refraction,  as  the 
case  may  be. 

With  a  metric  scale  determine  the  lengths  of  these  sines 
and  record  near  the  top  of  the  left-hand  page  in  a  tabular 
form  like  the  following : 


Fig.  58. 


TOTAL  REFLECTION  155 

OBS§RVATIONS 

Sine  of  first  angle  of  incidence cm. 

Sine  of  first  angle  of  refraction cm. 

Sine  of  second  angle  of  incidence       ....  cm. 

Sine  of  second  angle  of  refraction      ....  cm. 

Give  a  brief  account  of  the  geometrical  construction 
you  have  made.  No  further  drawing  is  necessary. 

Calculate  the  index  of  refraction  from  air  to  glass,  mak- 
ing use  of  the  measurements  made  on  each  side  of  the 
glass  ;  in  each  case  the  index  is  the  ratio  between  the 
sine  of  the  air  angle  and  the  sine  of  the  glass  angle. 
Tabulate  the  results. 

CALCULATED  RESULTS 

FIRST  CASE       SECOND  CASE       AVERAGE 

Index  of  Refraction 
Conclusion  : 

The  index  of  refraction  of  glass,  relative  to  air  is 


EXPERIMENT  45 

Total  Reflection 

OBJECT.  To  observe  total  reflection  and  determine  the  critical 
angle  for  glass. 

APPARATUS.  Flat  triangular  glass  prism,  about  7  cm.  on  a 
side  and  1  cm.  thick,  having  a  fine  line  drawn  across  the  center 
of  one  of  the  narrow  faces,  at  right  angles  to  the  broad  faces ;  4 
pins  ;  ruler  ;  protractor. 

Introductory : 

The  surface  of  a  glass  of  water,  viewed  obliquely  from 
below  through  the  water  itself,  becomes  bright  like  a  sil- 


156  LABORATORY  EXERCISES 

vered  mirror,  and  reflects  like  one,  when  a  certain  position 
has  been  reached.  Ice,  so  transparent  when  in  a  block, 
is  white  when  powdered.  Both  of  these  appearances  re- 
sult from  total  reflection.  Light  passing  through  a  dense 
medium,  as  water,  ice,  or  glass,  to  the  surface  of  a  medium 
less  dense,  as  air,  is  refracted  away  from  the  perpendicular. 
That  is,  the  angle  of  refraction,  under  these  circumstances, 
is  always  greater  than  the  angle  of  incidence.  When  the 
angle  of  incidence  reaches  a  certain  value,  the  refracted 
ray  will  lie  along  the  surface.  This  value  of  the  angle 
of  incidence  is  called  the  critical  angle.  If  the  angle  of 
incidence  increases  to  a  value  greater  than  the  critical 
angle,  the  light  is  totally  reflected,  instead  of  being  re- 
fracted. By  finding  experimentally  the  least  angle  of 
incidence  at  which  total  reflection  takes  place,  the  critical 
angle  can  be  found,  though  the  value  obtained  from  this 
experiment  is  an  approximate  one  only. 

Experimental : 

(a)  A  flat  triangular  prism  of  glass  is  placed  on  the 
center  of  the  right-hand  page  of  the  note-book.  The 
directions  which  follow  must  be  fully  understood  before 

the  experiment  is  begun 
and  must  be  exactly  fol- 
lowed to  secure  accurate 
results. 

Close  to  the  prism  on 
the  side  AS  insert  a  ver- 
tical pin  (j?)  firmly  in 

the    paper.       Near    the 

Hi?    59 

center  of   the   side  AC 

a  vertical  line  (0)  is  ruled  on  the  glass.  Placing  the  eye 
on  the  level  of  the  book,  move  the  head  until,  looking 
through  the  side  jB(7,  an  image  of  the  pin  (j?)  is  seen 


TOTAL  REFLECTION  157 

\ 

reflected  in  AC.     Note  the  appearance  of  AC  when  the 

head  is  in  this  position.  The  observed  image  is  the  result 
of  the  total  reflection  of  light  passing  through  the  glass 
from  ( jt?)  to  the  surface  A  0. 

(5)  Move  the  head  sideways  until  the  reflected  image 
of  the  pin  suddenly  disappears.  Continue  moving  the 
head  in  the  same  direction.  Does  the  image  again  ap- 
pear ?  Move  the  head  in  the  opposite  direction.  Does 
the  image  now  appear?  Beyond  the  point  where  the 
image  suddenly  disappeared,  the  light  rays  from  the  pin 
were  refracted  in  the  ordinary  way,  and  the  pin  might 
have  been  seen  by  looking  through  the  side  AC.  The 
particular  angle  of  incidence  on  the  surface  AC  of  rays 
from  the  pin  at  which  total  reflection  begins  and  refrac- 
tion ends,  is  called  the  critical  angle.  It  is  now  to  be 
determined. 

(c)  Keeping  the  side  AB  always  closely  against  the 
pin,  move  the  prism  and  the  head  into  various  positions, 
until  the  reflected  image  is  just  about  to  coincide  with 
the  vertical  mark  on  A  0  as  the  image  disappears.  When 
you  are  sure  that  you  have  located  this  position  correctly, 
insert  two  pins  (jt/)  and  (J/')  so  they  are  in  a  straight 
line  with  the  mark  on  AC,  as  seen  through  the  glass. 
These  pins,  then,  lie  in  the  line  taken  by  the  reflected 
ray  after  it  leaves  the  glass. 

Holding  the  prism  firmly  to  the  paper  with  the  left 
hand,  trace  its  outline  and  mark  on  AC  the  exact  loca- 
tion of  the  vertical  mark  (0)  on  that  face.  Removing 
the  prism,  draw  a  line  from  (j?)  to  the  marked  point  (0), 
representing  the  path  of  the  ray  incident  at  (0)  from  (JP). 
Draw  a  line  through  the  pins  (jt/)  and  (jt>")  to  BC,  and 
from  the  point  of  intersection  with  BC  draw  a  line  to  (0). 
Place  an  arrow  head  on  each  line  to  show  the  direction 
of  the  light  in  each  case. 


158  LABORATORY  EXERCISES 

At  (0)  erect  a  perpendicular  to  A  O.  With  a  protractor 
measure  the  angle  of  incidence  (which  is  the  critical  angle 
if  your  work  has  been  done  correctly)  and  the  angle  of 
reflection  in  the  glass.  Record  the  readings  of  the  pro- 
tractor on  the  figure. 

If  time  permits,  repeat  the  process  of  finding  the  critical 
angle,  using  the  next  page  of  the  note-book. 

No  table  of  observations  is  necessary,  as  all  observed 
results  are  recorded  on  the  drawing.  Write  a  brief  but 
complete  description  of  your  work,  referring  to  the  draw- 
ing, and  mention  any  conditions  that  were  observed  which 
are  not  shown  by  the  drawing.  No  sketch  of  the  apparatus 
is  necessary. 

Discussion : 

Through  what  kind  of  a  medium  must  light  pass  in 
order  to  be  totally  reflected  at  the  transparent  surface  of 
that  medium  ? 

Under  these  circumstances,  if  the  angle  of  incidence  be 
greater  than  the  critical  angle,  what  happens  to  the  light  ? 
If  the  angle  of  incidence  is  less  than  the  critical  angle, 
what  happens  ? 

In  total  reflection,  how  does  the  angle  of  incidence 
compare  with  the  angle  of  reflection  ? 

Conclusion : 

The  critical  angle  of  glass  is °. 


STUDY  OF  A  CONVERGING  LENS  159 

EXPERIMENT  46  A 

Study  of  a  Converging  Lens1 

OBJECT.  To  locate  the  principal  focus  of  a  converging  lens  and 
to  study  the  images  formed  by  such  a  lens,  when  the  lens  is  at 
different  distances  from  the  object. 

APPARATUS.  Double  convex  lens,  10  to  15  cm.  focus  ;  opaque 
screen ;  half-meter  stick ;  screen  with  translucent  window  (see 
description  under  "  Apparatus,"  page  166)  ;  meter  stick,  mounted 
as  shown  in  Fig.  61  ;  lens  and  screen  holders  to  slide  along  the 
meter  stick ;  incandescent  lamp  or  other  light ;  strip  of  paper 
more  than  twice  the  focal  length  of  the  lens. 

Introductory : 

Converging  lenses  are  among  the  most  useful  parts  of 
optical  instruments,  such  as  cameras,  telescopes,  and  pro- 
jection lanterns.  The  first  experience  of  most  boys  with 
a  converging  lens  is  the  handling  of  a  "burning  glass." 
The  parallel  rays  from  the  far  distant  sun  enter  the  lens, 
and  are  so  bent  in  direction  that  they  converge  to  a  point. 
This  point  of  convergence  of  parallel  rays  is  the  principal 
focus  of  the  lens.  The  focal  length  of  a  lens  is  the  dis- 
tance from  the  lens  to  the  principal  focus. 

When  we  look  through  a  converging  lens  at  an  object, 
we  see  an  image  of  the  object.  The  relations  of  the  ob- 
ject and  image  vary  according  to  the  position  of  the  object 
with  reference  to  the  principal  focus.  The  relations  are 
not  hard  to  find  and  are  interesting,  because  they  explain 
the  use  of  the  converging  lens  in  some  of  its  important 
practical  applications. 

1  This  experiment  is  essentially  qualitative  in  its  character.  Experi- 
ments 40  B  and  47  provide  for  a  quantitative  treatment  of  the  convex 
lens.  Either  one  kind  of  work  or  the  other  should  be  selected,  as  the 
performance  of  all  three  experiments  would  involve  unnecessary  repetition. 


160  LABORATORY  EXERCISES 

Experimental : 

(I)  The  Principal  Focus.  —  If  we  assume  that  the  rays 
from  a  fairly  distant  object  are  practically  parallel,  and 
that  these  rays  on  entering  the  lens  converge  to  the  prin- 
cipal focus,  the  location  of  a  sharp  image  of  the  distant 
object  on  a  screen  tells  us  the  position  of  the  principal 
focus.  Accordingly,  set  the  lens  on  one  of  the  main  divi- 
sions of  a  half-meter  stick,  and  move  the  screen  until  the 
most  distant  bright  object  which  can  be  seen  through  the 
window  is  sharply  focused  on  the  screen. 
Note  the  distance  between  the  lens  and  the 
screen  (principal  focus).  Record  this  focal 
length  in  the  table  of  observations  near  the 
top  of  the  left-hand  page.  Take  two  more 

OzJ — ^    readings,  moving  the  lens  and  screen  each 
iiv7i  i  %      .  ,  ,  f  ,.  ,    . 

time.     Record  these  readings,  and  the  aver- 
age of  the  three,  which  will  be  considered 
the  focal  length.     A  simple  and  very  convenient  form  of 
lens  holder  is  shown  in  Fig.  60. 

(II.)  Relations  of  Object  and  Image.  —  On  a  strip  of 
paper  draw  a  line  just  twice  the  focal  length  of  the  lens  in 
length ;  in  the  middle  of  the  line  place  a  mark,  the  dis- 
tance of  which  from  either  end  will  be  equal  to  the  focal 
length.  All  distances  in  the  remaining  portion  of  the 
experiment  are  to  be  measured  in  terms  of  the  focal  length 
of  the  lens,  by  means  of  this  marked  line,  and  not  by 
means  of  the  numbers  on  the  meter  stick. 

At  one  end  of  the  meter  stick  place  an  incandescent 
lamp  or  other  light,  and  directly  in  front  of  the  light  a 
screen  with  a  translucent  window  in  it  to  serve  as  an 
object  (Fig.  61). 

(a)  Set  the  lens  at  its  focal  length  from  the  illuminated 
screen.  The  object  is  now  at  the  principal  focus  of  the 


STUDY  OF  A  CONVERGING  LENS 


161 


lens.  Move  the  opaque  screen  on  the  other  side  of  the 
lens,  and  note  whether  or  not  an  image  is  formed  on  this 
screen.  The  formation  of  an  image  means  that  the  rays 
of  light  leaving  the  lens  converge.  If  an  image  is  not 
formed,  the  rays  leaving  the  lens  are  either  parallel  or 
divergent.  When  the  object  is  at  the  principal  focus,  what 
is  the  direction  of  the  ray 9  leaving  the  lens  ?  (Recall  the 
method  of  finding  the  principal  focus.) 

(6)  Move  the  lens  nearer  the  illuminated  screen  than 
in  (a).  The  object  is  now  within  the  principal  focus. 
Move  the  screen  to  ascertain  whether  or  not  an  image  is 


Fig.  61. 

formed.  Look  through  the  lens  at  the  illuminated  screen 
and  describe  its  appearance.  In  this  case  what  do  you 
think  is  the  direction  of  the  rays  leaving  the  lens  ?  Explain. 
(c)  Place  the  lens  so  that  the  object  is  at  a  distance  of 
twice  the  focal  length.  Place  the  screen  at  an  equal  dis- 
tance on  the  other  side  of  the  lens.  Is  the  image  on  the 
screen  erect  or  inverted  ?  J  Is  it  larger  or  smaller  than  the 
object  ?  When  the  object  is  at  twice  the  focal  length  from  the 
lens  compare  (1)  the  relative  distances  from  the  lens  of  object 
and  image,  (2)  the  relative  size  of  object  and  image.  At 

1  In  case  a  sharp  image  is  not  formed  at  twice  the  focal  length,  find  the 
shortest  distance  between  the  object  and  the  screen  at  which  a  distinct 
image  of  the  object  can  be  formed  on  the  screen.  Compare  the  object 
and  image  distances  with  each  other  and  with  twice  the  focal  length. 


162  LABORATORY  EXERCISES 

what  distance  from  a  camera  lens  would  you  place  a  drawing 
in  order  to  obtain  a  photographic  copy  of  the  same  size  ? 

(d)  Move  the  lens  in  a  little  toward  the  object,  so  that 
it  is  at  a  distance  from  the  object  greater  than  the  focal 
length,  but  less  than  twice  the  focal  length.     Move  the 
opaque  screen  until  a   sharp    image   of   the   illuminated 
screen  is  obtained  on   it.      Alongside   the   line  already 
drawn  on  your  strip  of  paper,  lay  off  another  line  whose 
length  is  the  distance  between  the  lens  and  the  image  in 
this  case.     On  this  line  also  mark  the  object  distance. 

Compare  the  image  distance  with  twice  the  focal  length. 
Note  the  relative  sizes  of  object  and  image.  When  an 
object  is  at  a  distance  from  a  lens  greater  than  the  focal 
length,  and  less  than  twice  the  focal  length,  (1)  state  the  gen- 
eral location  of  the  image  in  terms  of  the  focal  length,  (2) 
compare  the  image  and  object  as  to  size. 

(e)  Move  the  lens  to  a  point  whose  distance  from  the 
object  is  equal  to  the  image  distance  obtained  in  (rf).     The 
object  distance  is  now  greater  than  twice  the  focal  length. 
Slide   the    opaque  screen   into  a  position  where  a  sharp 
image  is  formed.     Note  the  relative  sizes  of  object  and 
image.     Beside  the  line  drawn  in  (<T),  lay  off  another  line 
on  which  the  object  and  image  distance  in  this  case  are 
marked.     Compare  the  image  distance  in  this  case  with 
twice  the  focal  length  and  with  the  focal  length.      When 
an  object  is  at  a  distance  from  a  lens  greater  than  twice  the 
focal  length,  (1)  state  the  general  location  of  the  image,  (2) 
compare  the  object  and  image  as  to  size.      Conjugate  foci  of 
a  lens  are  points  so  located  in  reference  to  the  lens  that, 
if  the  object  is  placed  at  either  point,  the  image  will  be 
located  at  the  other.       State  two  cases  of  conjugate  foci 
shown  in  this  experiment. 

In  a  table  near  the  top  of  the  left-hand  page,  the  read- 
ings of  focal  length  are  to  be  entered.  Immediately 


STUDY  OF  A  CONVERGING  LENS  163 

beneath  this  the  strip  of  paper  on  which  the  various  dis- 
tances have  been  recorded,  is  to  be  pasted  by  one  end. 
Each  line  on  the  strip  should  be  marked  to  indicate  just 
what  distances  it  records. 

OBSERVATIONS 

128  AVERAGE 

Focal  length  of  lens  cm.     em.      cm.     cm. 

A  brief  description  of  the  work  done  in  each  part  of  the 
experiment  should  folio  w  the  "  Observations. "  Any  obser- 
vations not  recorded  on  the  strip  or  in  the  table  should  be 
included  in  the  description.  The  description  should  be 
accompanied  by  a  drawing  showing  the  apparatus  when 
the  principal  focus  was  being  determined,  and  a  drawing 
showing  the  location  of  lens,  screens,  and  lamp  in  position 
for  one  of  the  cases  where  an  image  was  formed. 

Discussion : 

Answer  under  this  heading  all  questions  in  italics  con- 
tained in  the  experimental  directions. 

Where  will  the  screen  for  a  stereopticon  be  located  with 
reference  to  the  focal  length  of  the  objective  lens  ?  Where 
will  the  lantern  slide  be  located  ? 

Conclusion  i 

What  is  the  least  distance  from  a  converging  lens  at 
which  an  object  can  be  placed  in  order  that  a  real  image 
may  be  formed  ? 

State  a  general  relation  between  the  sizes  of  the  object 
and  image,  and  their  respective  distances  from  the  lens. 


164  LABORATORY  EXERCISES 

• 
EXPERIMENT    46  B 

Focal  Length  of  a  Converging  Lens 

OBJECT.  To  locate  the  principal  focus  and  determine  the  focal 
length  of  a  converging  lens. 

APPARATUS.  Double  convex  lens,  10  to  15  cm.  focus;  lens 
holder ;  screen ;  screen  holder ;  half-meter  stick ;  the  lens  and 
screen  holders  should  fit  and  slide  along  the  half-meter  stick. 

Introductory : 

A  camera  may  be  made  which,  will  take  fairly  sharp 
pictures  of  all  objects  more  than  100  ft.  or  so  away.  This 
is  because  objects  at  a  greater  distance  than  that  send 
practically  parallel  rays  into  the  lens  and  so  form  the 
image  at  the  principal  focus  of  the  lens.  By  assuming 
that  the  rays  entering  the  lens  from  fairly  distant  objects 
do  converge  to  the  principal  focus,  we  may  locate  the 
focus  by  getting  the  image  of  a  distant  building  on  a 
screen,  which  will  then  be  at  the  principal  focus.  The 
focal  length  of  a  lens  is  the  distance  from  the  lens  to  the 
principal  focus. 

Experimental : 

Set  the  lens  on  a  half-meter  stick  and  move  the  screen 
until  the  most  distant  bright  object   which  can  be  seen 
through    the   window   is   sharply 
focused  on  the  screen. 

Take  three  readings,  moving 
both  lens  and  screen  each  time, 
recording  in  each  case  the  position 
of  the  lens  and  the  screen  in  the 
table  of  observations  near  the  top 
Fig.  62.  of  the  left-hand  page. 


FOCAL  LENGTH  OF  A  CONVERGING  LENS       165 
OBSERVATIONS 

TRIAL  POSITION  OF  LENS  POSITION  OP  SCREEN  NUMBER  OF  LENS 

1 

2  

3  

Make  a  drawing  of  the  apparatus  and  show  by  short 
dash  lines  the  path  of  the  light  rays  before  and  after 
passing  through  the  convex  lens.  Briefly  describe  the 
method  of  the  experiment. 

In  the  table  of  calculated  results  at  the  top  of  the  right- 
hand  page,  record  the  average  distance  between  the  lens 
and  the  principal  focus  as  the  focal  length. 

If  time  permits,  determine  the  focal  length  of  a  second 
lens,  recording  it  in  the  last  line  of  the  table  of  calculated 
results. 

CALCULATED  RESULTS 

TRIAL    123 

Distance  betiveen  lens  and  screen 

Focal  lengtK  of  lens  No.    (Average  0/1,2,  &  3)  .. 

Focal  length  of  lens  No.    

Discussion : 

Define  (a)  the  principal  focus,  (6)  the  principal  focal 
length.  Why  is  the  most  distant  object  available  selected  ? 
Why  is  the  convex  lens  spoken  of  as  a  converging  lens  ? 

Conclusion : 

The  principal  focal  length  of  lens  No. is . 


166  LABORATORY  EXERCISES 


EXPERIMENT   47 

Conjugate  Foci  of  a  Converging  Lens 

OBJECT.  To  determine  the  conjugate  foci  of  a  converging  lens 
and  their  relation  to  the  principal  focus. 

APPARATUS.  Double  convex  lens  ( 10  to  15  cm.  focal  length); 
lens  holder  ;  opaque  screen ;  screen  holder ;  meter  stick,  sup- 
ported in  the  slots  of  two  wooden  blocks ;  opaque  screen,  with 
round  or  square  window  cut  in  it,  over  which  is  pasted  a  piece  of 
very  thin  paper  with  ink  lines  ruled  across  it  at  right  angles,  and 
with  an  ink  mark  in  one  of  the  four  spaces  formed  by  the  inter- 
secting lines  ;  candle  or  incandescent  lamp  to  be  placed  behind  the 
translucent  window  (see  Fig.  61,  page  161). 

Introductory : 

When  a  pencil  of  light  diverges  from  a  point  and  is  in- 
cident on  a  lens,  it  is  brought  to  a  focus  by  the  lens  at  a 
point  on  the  axis  passing  through  the  radiant  point  from 
which  the  light  came.  The  radiant  point  and  the  focal 
point  are  conjugate  foci  of  the  lens.  Conjugate  foci  of  a 
lens  are  points  so  located  with  reference  to  the  lens  that, 
if  the  object  is  placed  at  either  point,  the  image  will  be 
located  at  the  other. 

Conjugate  foci  may  be  located  by  determining  the  two 
positions  between  an  object  and  a  screen  where  a  lens  may 
be  placed  so  as  to  form  a  sharp  image  on  the  screen.  In 
such  positions,  an  important  relation  exists  between  the 
distance  of  the  object  from  the  lens,  the  distance  of  the 
image  from  the  lens,  and  the  focal  length  of  the  lens. 


CONJUGATE  FOCI  OF  A  CONVERGING  LENS      167 

Experimental : 

Arrange  the  apparatus  as  in  Fig.  61.  Then  adjust  the 
position  of  the  lens  so  that  a  distinct  image  of  the  illumi- 
nated paper  will  be  formed  on  the  opaque  screen.  Is  the 
image  erect  or  inverted  ?  Real  or  virtual  ? 

Measure  the  diameter  of  the  object  and  of  the  image. 
Record  in  tabular  form  near  the  top  of  the  left-hand  page. 

Record  the  position  on  the  meter  stick  of  the  object,  the 
lens,  and  the  image. 

Leaving  the  object  and  screen  in  position,  move  the  lens 
until  you  find  another  position  for  it,  at  which  the  lens 
will  again  produce  a  distinct  image.  Make  the  same  ob- 
servations as  before,  and  record. 

OBSERVATIONS 

i  ir 

Position  of  object cm. cm. 

Position  of  lens cm. cm. 

Position  of  image cm. cm. 

Diameter  of  object cm. cm. 

Diameter  of  image cm.  cm. 

Image  —  erect  or  inverted    .     .     .      

Image — real  or  virtual       .     ..     .     

Number  of  lens 

Make  a  simple  drawing,  showing  the  arrangement  of 
apparatus,  and  describe  how  it  was  used. 

In  case  you  do  not  know  the  focal  length  of  the  lens, 
determine  it  by  the  method  given  in  Experiment  46  B,  on 
page  164. 

Place  the  table  for  the  calculated  results  at  the  top  of 
the  right-hand  page,  and  make  the  calculations  indicated. 
All  reciprocals  should  be  worked  out  as  decimals,  the  re- 
sult being  carried  to  four  decimal  places. 


168  LABORATORY  EXERCISES 

CALCULATED  RESULTS 

i  ii 

Distance  of  object  from  lens      .     .     cm.  cm. 

Distance  of  image  from  lens     .     .     cm.  cm. 

1 
Object  distance 

1 
Image  distance 


Object  distance      Image  distance 

Principal  focal  length  of  lens  .     .      cm. 

1 

Focal  length  of  lens 

Discussion : 

What  is  the  relation  between  the  diameters  of  the  object 
and  the  image,  and  their  respective  distances  from  the 
lens? 

Conclusion : 

Compare  the  sum  of  the  reciprocals  of  the  image  and 
object  distances  with  the  reciprocal  of  the  principal  focal 
length. 


MAGNIFYING  POWER  OF  A  LENS  169 

EXPERIMENT  48 

Magnifying  Power  of  a  Lens 

OBJECT.  To  find  the  ratio  of  the  diameter  of  an  object  viewed 
with  the  unaided  eye  to  the  diameter  of  the  image  seen  through  a 
converging  lens. 

APPARATUS.  Two  double  convex  lenses,  of  5  and  10  cm. 
focal  length  respectively ;  half-meter  stick ;  opaque  screen ;  lens 
holder  and  screen  holder  to  slide  along  the  meter  stick ;  piece  of 
cardboard,  2"  x  3",  covered  on  one  side  with  black  paper,  and* 
with  a  square  hole  in  the  center  1  cm.  on  a  side ;  paper  metric 
scale ;  ring  stand  with  two  small  condenser  or  burette  clamps, 
with  cork-lined  jaws. 

Introductory : 

Double  convex  lenses  are  used  in  certain  optical  instru- 
ments because  the  images  produced  by  them  are  larger 
than  the  objects  viewed.  The  ratio  of  the  diameter  of  the 
image  to  the  diameter  of  the  object  is  the  magnifying 
power  of  the  lens. 

By  the  size  of  an  object,  we  mean  that  apparent  to  the 
unaided  eye.  It  has  been  found,  however,  that  the 
majority  of  people  obtain  the  most  distinct  vision  when 
the  object  is  25  cm.  from  the  eye.  Accordingly,  if  we 
take  for  our  object  a  line,  it  should  be  viewed  at  the  dis- 
tance of  most  distinct  vision  (25  cm.).  This  line  will 
appear  longer  when  seen  through  a  converging  lens.  The 
ratio  of  the  apparent  length  of  the  line  as  seen  through 
the  lens  to  the  length  of  the  line  seen  with  the  unaided 
eye,  is  the  magnifying  power  of  the  lens.  In  this  man- 
ner we  are  comparing  the  diameter  of  an  object  with  that 
of  its  image. 


170 


LABORATORY  EXERCISES 


Experimental : 

(a)  Set  the  lens  of  greater  focal  length  on  some  even 
centimeter  division  of  the  half-meter  stick  pointing 
toward  the  window.  On  the  other  end  of  the  stick  place 
the  screen,  and  move  it  toward  the  lens  until  the  most 
distant  bright  object  which  can  be  seen  through  the  win- 
dow is  sharply  focused  on  tHe  screen.  Note  the  distance 
between  the  lens  and  the  screen 
(principal  focal  length).  Record 
this  focal  length  in  the  table  of 
observations  placed  near  the  top 
of  the  left-hand  page. 

Place  the  lens  horizontally 
(Fig.  63)  in  the  jaws  of  a  clamp 
on  a  ring  stand,  tightening  the 
clamp  just  enough  to  hold  the 
lens,  but  not  enough  to  crack 
the  glass.  Adjust  the  clamp  in 
height  so  that  the  lens  is  25  cm. 
above  the  table  top. 

Support  with  another  clamp 
the  cardboard  diaphragm,  so  that 
its  square  opening  is  just  at  the  principal  focus  of  the  lens. 
Place  a  paper  metric  scale  on  the  table  below  the  opening. 
Look  down  through  the  lens  at  the  scale  with  one  eye, 
while  viewing  the  scale  at  the  same  time  with  the  other 
(unaided)  eye.  Note  how  many  millimeter  divisions  seen 
with  the  unaided  eye  are  apparently  covered  by  the  width 
of  the  opening.  A  little  practice  will  enable  you  to  make 
the  comparison  without  any  straining  of  the  eyes. 

Record  the  apparent  width  in  millimeters  in  the  table 
of  observations.  Measure  in  millimeters  the  actual  width 
of  the  opening,  and  record.  This  actual  width  is  the  num- 


Fig.  63. 


MAGNIFYING  POWER  OF  A  LENS  171 

ber  of  millimeter  divisions  which  the  unaided  eye  could 
see  through  the  square  opening  if  it  were  placed  upon  the 
scale. 

(5)  Repeat  the  measurements  of  part  (a),  using  the 
lens  of  shorter  focal  length. 

OBSERVATIONS 
Width  of  opening  in  diaphragm       .     .     .     mm. 

PART  (a)  PART  (&) 

Focal  length  of  lens      .     .     .     _.  cm.    cm. 

Apparent   width   of   opening 

seen  through  lens      .     .     .     mm. mm. 

Make  a  drawing  showing  the  relative  position  of  the 
eyes,  the  lens,  the  opening  in  the  diaphragm,  and  the 
metric  scale  when  the  comparison  was  made.  Describe 
the  method  of  making  the  comparison. 

The  ratio  between  the  number  of  millimeter  divisions 
which  can  apparently  be  seen  through  the  opening  when 
the  lens  is  used,  and  the  number  of  such  divisions  visible 
through  the  opening  to  the  unaided  eye,  is  the  magnifying 
power  of  the  lens.  Calculate  the  magnifying  power  of  the 
lenses  used  in  (a)  and  (6).  Record  your  results  in  the 
table  of  calculated  results  at  the  top  of  the  right-hand 

page. 

CALCULATED  RESULTS 

Magnifying  power  of  lens  in  (a)     .     .     .     times 

Magnifying  power  of  lens  in  (6)     *     .     .     ..times 

Discussion : 

Why  is  the  metric  scale  viewed  at  a  distance  of  25  cm.? 
Is  the  lens  of  shorter  focal  length  more  desirable  for  a 
simple  magnifier  than  that  of  longer  focal  length  ?  Ex- 
plain. 


172  LABORATORY  EXERCISES 

Conclusion : 

Complete  the  statement : 

The  magnifying  power  of  a  lens  is  the  ratio  of 


EXPERIMENT   49  A* 

The  Astronomical  Telescope 

OBJECT,  (a)  To  construct  and  learn  the  operation  of  a  simple 
astronomical  telescope ;  (&)  to  find  its  magnifying  power. 

APPARATUS.  Double  convex  lens  of  short  focal  length  (5  or 
10  cm.)  ;  lens  holder  to  slide  along  half-meter  stick;  lens  of  long 
focal  length,  not  over  40  cm.  (a  reading  glass  may  be  used)  ; 
holder  or  clamp  for  supporting  lens;  cardboard  screen  with  trans- 
lucent window  1"  square ;  screen  holder  to  slide  along  half-meter 
stick ;  half-meter  stick ;  ring  stand ;  burette  clamp ;  strip  of 
white  cardboard,  20"  x  3",  ruled  with  black  vertical  lines  1"  apart 
and  |"  thick;  strip  of  white  cardboard,  about  5"  x  2",  with  a  black 
arrow  2"or  3"  long  drawn  along  the  middle. 

Introductory : 

An  astronomical  telescope  in  its  simplest  form  consists 
of  two  double  convex  lenses  at  the  opposite  ends  of  an 
opaque  tube,  with  some  device  for  varying  the  length  of 
the  tube.  The  lens  through  which  the  eye  looks  is  gener- 
ally smaller  than  the  lens  at  the  end  of  the  tube  point- 
ing towards  the  object  to  be  viewed.  These  two  lenses, 
moreover,  will  be  found  to  differ  considerably  in  focal 
length. 

1  Experiments  49  A  and  49  B  are  similar  in  method  and  afford  similar 
training.  It  is  recommended  that  only  one  of  them  be  performed,  unless 
there  is  abundant  laboratory  time. 


THE  ASTRONOMICAL  TELESCOPE  173 

To  understand  the  operation  of  an  astronomical  tele- 
scope, we  must  find  why  two  lenses  are  used;  w)iy  the 
lenses  must  be  so  different  in  focal  length ;  what  is 
meant  by  bHnging  the  instrument  into  focus.  The  first 
step  toward  answering  these  questions  is  to  determine  the 
focal  length  of  each  lens.  Then  by  mounting  them  in 
suitable  relative  positions,  we  can  improvise  a  telescope 
and  determine  the  principles  of  its  operation. 

Experimental : 

•  (a)  Focal  Length  of  the  Lenses. — Take  the  lens  of  short 
focal  length,  which  is  to  be  used  as  the  eyepiece  of  the  tele- 
scope, and  mount  it  on  the  end  of  a  half-meter  stick  point- 
ing toward  a  window.  Move  a  screen  on  the  stick  toward 
the  lens,  until  the  most  distant  bright  object  seen  through 
the  window  is  sharply  focused  on  the  screen.  Is  the 
image  erect  or  inverted  ?  Measure  on  the  half-meter  stick 
the  distance  between  the  lens  and  the  screen.  Record 
this  focal  length  in  a  table  of  observations  near  the  top  of 
the  left-hand  page. 

Mount  the  other  lens  (the  objective)  over  one  end  of 
the  half-meter  stick,  by  means  of  the  clamps  and  ring 
stand,  and  determine  its  focal  length  in  a  similar  manner, 
and  record. 

(6)  Use  of  the  Lenses.  —  Leaving  the  objective  focused' 
on  the  screen,  mount  the  eyepiece  on  the  meter  stick,  on 
the  other  side  of  the  screen,  so  that  the  centers  of  the  two 
lenses  are  on  the  same  horizontal  line.  (Fig.  64.) 

Looking  through  the  eyepiece,  move  it  along  the  stick 
until  you  can  see  distinctly  the  image  thrown  on  the  screen 
by  the  objective.  Record  the  distance  of  the  eyepiece  from 
the  screen.  Does  the  image  viewed  through  the  eyepiece 
appear  larger  or  smaller  than  the  image  that  the  unaided 
eye  can  see  on  the  screen  ? 


174 


LABORATORY  EXERCISES 


Leaving  the  lenses  undisturbed,  remove  the  screen. 
Again  look  through  the  eyepiece.  Can  you  see  the  image 
of  the* distant  object?  Record  the  distance  between  the 
objective  and  the  eyepiece.  •* 

(c)  Focusing.  —  Shift  the  meter  stick  in  the  clamp  a  few 
centimeters.  Move  the  eyepiece  until  you  can  see  dis- 
tinctly through  it  the  image  of  the  distant  object.  This 

is  the  method  of 
focusing  the  eye- 
piece of  a  tele- 
scope on  the  im- 
age of  a  distant 
object  projected 
through  the  ob- 
jective. Record 
the  distance  be- 
tween the  objec- 
tive and  the  eye- 
piece. 

(d}  Magnify- 
ing Power.  —  On 
the  most  conven- 
ient and  distant 
wall  of  the  room, 
place  as  an  object,  a  black  arrow  on  a  strip  of  white  card- 
board. The  arrow  should  be  in  the  same  horizontal  plane 
as  the  centers  of  the  lenses  of  the  telescope. 

Focus  the  telescope  ,on  the  black  arrow.  Have  another 
student  stand  at  the  distant  wall  and  move  the  scale  with 
the  black  ruled  lines  down  toward  the  arrow  while  you 
are  looking  through  tjie  telescope.  By  using  both,  eyes 
at  the  same  time,  you  will  be  able  to  see  how  many  divi- 
sions of  the  scale  are  equal  to  the  apparent  length  of  the 
arrow,  as  seen  through  the  telescope.  Measure  the  real 


Fig.  64. 


THE  ASTRONOMICAL  TELESCOPE  175 

length  of  the  arrow  in  divisions  of  the  ruled  scale. 
Record  both  measurements  in  the  table  of  observations. 
How  many  times  is  the  length  of  the  arrow  magnified  by 
the  telescope  ?  Record  this  magnifying  power  in  the  table 
of  calculated  results. 

OBSERVATIONS 

Part  (a)  Focal  length  of  eyepiece       .     .     .  cm. 
Focal  length  of  objective      .      .     .  cm. 
Part  (6)  Distance  of  eyepiece  from  screen  .  cm. 
Distance  between  objective  and  eye- 
piece    cm. 

Part  (c)  Distance  between  objective  and  eye- 
piece          cm. 

Part  (d)  Actual  length  of  arrow   ....  divisions 
Apparent  length  of  arrow  through 

divisions 


Make  a  simple  outline  drawing,  showing  the  arrange- 
ment of  the  lenses  in  your  telescope.  Describe  briefly 
the  steps  you  took  in  each  part  of  the  experiment. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 

Sum  of  focal  lengths  of  objective  and  eyepiece          cm. 
Magnifying  power  of  telescope    .     .     .     «     .         times 
Ratio  of  focal  length  of  objective  to 
focal  length  of  eyepiece       .  '  .     . 


Discussion : 

Why  is  a  lens  of  long  focal  length  used  as  the  objective 
of  an  astronomical  telescope?  What  is  the  purpose  of  the 
eyepiece  (the  lens  of  short  focal  length)  ?  Compare  the 


176  LABORATORY  EXERCISES 

observed  magnifying   power  with  the  ratio  of  the  focal 
lengths. 

Conclusion : 

Complete  this  statement: 

When  an  astronomical  telescope  is  focused  on  a  distant 
object,  the  distance  between  the  objective  and  the  eye- 
piece is  equal  to  the 


EXPERIMENT    49  B 

The  Compound  Microscope 

OBJECT.  To  construct  a  compound  microscope  and  to  determine 
its  magnifying  power. 

APPARATUS.  Two  double  convex  lenses  of  short  focal  length 
(about  5  cm.)  ;  lens  holder  and  screen  holder,  to  slide  along  a 
half-meter  stick ;  half-meter  stick ;  piece  of  cardboard,  with  a 
black  arrow  1  cm.  in  length  drawn  on  the  middle  of  one  side ; 
ring  stand  with  two  cork-lined  burette  or  small  condenser  clamps  ; 
paper  metric  scale. 

Introductory : 

The  compound  microscope  in  its  simplest  form  consists 
of  two  converging  lenses  of  short  focal  length,  mounted 
a  suitable  distance  apart  and  usually  at  the  ends  of  an 
opaque  tube.  The  objects  viewed  with  the  microscope 
are  small  ones  and  they  are  placed  under  the  lens  known 
as  the  objective  and  just  beyond  its  principal  focus.  The 
image  formed  by  the  objective  is  viewed  through  the  other 
lens  (the  eyepiece}.  The  magnifying  power  depends  on 
the  focal  lengths  of  the  two  lenses  used  and  also  on  the 
distance  between  them. 


THE  COMPOUND  MICROSCOPE 


177 


The  magnifying  power  may  be  denned  as  the  ratio 
between  the  diameter  of  the  image  seen  through  the 
microscope  and  the  diameter  of  the  object  viewed  with  the 
unaided  eye.  We  shall  view  a  little  ruled  arrow  through 
the  microscope,  while  the  other  eye  is  looking  at  a  metric 
scale  placed  beside  the  arrow. 

Experimental : 

(a)  Focal  Length  of  the  Lenses.  —  Take  one  of  the  lenses 
for  the  eyepiece  and  mount  it  on  a  half-meter  stick  near 
the  end  pointing  toward  a  window.  Move  a  screen  on 
the  meter  stick  toward  the  lens  until  the  most  distant 
bright  object  to  be  seen  through  the  window  is  sharply 
focused  on  the  screen.  Then  measure  on  the  meter  stick 
the  distance  between  the  lens 
and  the  screen.  Record  this 
focal  length  in  the  table  of 
observations  near  the  top  of 
the  left-hand  page. 

Determine  similarly  the 
focal  length  of  the  other  lens 
(the  objective)  and  record 
the  distance  in  the  table. 

(6)  Construction.  —  Place 
on  the  base  of  the  ring  stand 
a  piece  of  white  cardboard 
with  its  drawing  of  a  little 
arrow  for  the  object. 

Carefully  mount  each  of 
the  lenses  in  the  cork-lined 
jaws  of  a  small  clamp  and  arrange  on  the  ring  stand  as 
shown  in  Fig.  65.  The  objective  should  be  fixed  above 
the  object  at  a  height  greater  than  the  focal  length  of 
that  lens,  but  at  less  than  twice  the  focal  length. 


Fig.  65. 


178  LABORATORY  EXERCISES 

Looking  through  the  eyepiece,  move  that  lens  up  and 
down  until  a  sharply  defined,  black  image  of  the  little 
arrow  is  seen.  Is  the  image  real  or  virtual  ?  In  what 
two  respects  is  the  image  different  from  the  object? 
Measure  the  height  of  the  objective  above  the  object  and 
the  vertical  distance  between  the  centers  of  the  two 
lenses.  Record  these  distances  in  the  table.  Leave  the 
microscope  focused  for  part  (<?). 

(c)  Magnifying  Power.  —  Place  a  paper  metric  scale 
near  the  little  arrow  and  parallel  to  it.  With  one  eye  look 
through  the  microscope  at  the  arrow,  while,  at  the  same 
time,  with  the  other  (unaided)  eye  you  are  viewing  the 
metric  scale.  Slide  the  metric  scale  so  that  you  can 
measure  the  length  of  the  arrow,  as  it  appears  through 
the  microscope.  The  divisions  of  the  scale  should  not 
look  magnified.  Record  the  apparent  length  of  the  ar- 
row in  millimeters.  Measure  the  actual  length  of  the 
arrow  with  the  scale  and  record  it  in  the  table.  What 
is  the  apparent  magnifying  power  of  your  microscope  ? 

OBSERVATIONS 

Focal  length  of  the  eyepiece cm. 

Focal  length  of  the  objective     ......  cm. 

Distance  of  objective  from  object cm. 

Distance  between  centers  of  lenses  when  micro- 
scope is  focused cm. 

Characteristics  of  image  (enlarged  or  dimin- 
ished)   

Characteristics  of  image  (erect  or  inverted) 

Apparent  length  of  arrow  through  microscope  .         mm. 

Actual  length  of  arrow. mm. 

Make  a  simple  diagram  showing  the  relative  positions 
of  the  eye,  the  two  lenses,  and  the  object.  Describe, 


DISPERSION  OF  LIGHT  BY  A  PRISM  179 

with   reference  to  the  drawing,  the  work  in   (6).     De- 
scribe also  how  you  determined  the  magnification  in  (V). 

CALCULATED  RESULTS 
Magnifying  power  of  microscope    ....  times. 

Discussion : 

Why  should  not  the  object  be  placed  at  the  principal 
focus  of  the  objective  ?  When  the  object  is  beyond  the 
principal  focus,  but  not  distant  twice  the  focal  length 
from  the  objective,  how  does  the  image  compare  in  size 
with  the  object  ?  Is  this  image  real  or  virtual  ?  Upon 
what  is  the  eyepiece  focused  ?  Compare  the  distance 
between  the  lenses  with  the  focal  length  of  the  eyepiece. 
Explain  how  this  distance  affects  the  magnifying  power 
of  the  microscope. 

Conclusion : 

State  the  essentials  in  the  construction  of  a  compound 
microscope.  How  must  the  eyepiece  and  the  objective 
be  placed  to  secure  magnification  ? 


EXPERIMENT    50 

Dispersion  of  Light  by  a  Prism 

OBJECT.  To  observe  the  effect  of  a  triangular  glass  prism  on  a 
beam  of  white  light. 

APPARATUS.  Triangular  glass  prism,  60°  ;  opaque  covering  for 
the  upper  half  of  laboratory  window,  with  a  slit  6  in.  x  f  in. ; 
second  opaque  covering,  with  f "  slits  arranged  as  in  Fig.  67. 

Introductory : 

When  we  look  through  glass  prisms,  such  as  are  some- 
times hung  from  the  bottom  of  a  lamp  shade,  we  notice  that 


180 


LABORATORY  EXERCISES 


the  outlines  of  objects  show  a  fringe  of  color.  When  the 
sun  begins  to  shine  before  the  rain  stops  falling,  a  rain- 
bow, consisting  of  a  band' of  the  same 
colors  seen  through  the  glass  prism, 
appears  in  the  sky.  In  both  of  these 
cases  white  light  has  been  broken  up 
into  colors,  by  passing  through  a  trans- 
parent medium  more  dense  than  air. 


Experimental : 

(a)  The  upper  part  of  the  laboratory 
window  will  have  an  opaque  covering, 
in  which  a  narrow  slit  has   been  cut. 
Fig  66  Take  a  position  from  which  the  sky  can 

be  seen  through  the  slit.  Close  one 
eye  and,  holding  the  prism  in  front  of  the  other  with  one 
edge  pointing  toward  the  slit,  rotate  the  prism  slowly 
until  the  slit  appears  as  a  band  of  color.  Name  the  colors 
distinctly  seen,  in  the  order  in  which  they  appear  to  you. 
Since  the  different  col- 
ors appear  in  different 
positions,  what  must  be 
true  of  the  amount  of 
bending  of  each?  No- 
tice carefully  the  posi- 
tion of  the  faces  of  the 
prism  and  see  if  you  can 
determine  which  of  the 
colors  is  most  refracted. 
(J)  On  the  upper  half 
of  another  laboratory 
window  there  has  been 


i-ig.  67. 


placed  an  opaque  covering  with  three  pairs  of  slits  ar- 
ranged as  in  Fig.  67.     Holding  the  prism  in  front  of 


FIXED  POINTS  OF  A  THERMOMETER  181 

the  eye  as  before,  look  at  the  slits.  Note  the  overlap- 
ping of  the  spectra.  Find  a  case  in  which  there  is  vis- 
ible a  color  not  evident  in  the  spectrum  as  seen  in  (a). 
What  colors  by  their  overlapping  produced  this  new 
color?  Can  you  find  another  distinct  color  formed  by 
the  combining  of  the  light  rays  of  two  different  colors  ? 
In  which  case  do  you  find  a  streak  of  white  produced  by 
the  overlapping  spectra.  What  colors  combined  to  form 
this  whitish  light  ? 

Make  one  sketch  showing  how  the  prism  was  held  in 
front  of  the  eye,  and  two  diagrams  showing  the  arrange- 
ment of  the  slits  on  the  opaque  coverings.  Describe  the 
experiment  with  reference  to  these  drawings,  stating  the 
results  in  each  case.  The  description  may  be  shortened 
by  the  use  of  further  diagrams  in  which  the  colors  of  the 
spectra  are  mapped. 

Conclusion : 

What  happens  to  a  ray  of  white  light  in  passing  through 
a  glass  prism  ?  How  may  other  colors  be  formed  from 
the  primary  colors  of  the  solar  spectrum  ? 


EXPERIMENT    51 

Fixed  Points  of  a  Thermometer 

OBJECT.  To  test  the  boiling  and  the  freezing  points  on  a 
mercury  thermometer. 

APPARATUS.  Steam  boiler  with  bent  glass  delivery  tube ; 
1-hole  rubber  stopper  tightly  fitting  the  top  of  the  boiler  chimney; 
hydrometer  jar;  thermometer,  —10°  to  1 10°C. ;  glass  funnel; 
cylindrical  or  other  jar  to  support  funnel ;  burner ;  supply  of 
cracked  ice. 


182 


.     LABORATORY  EXERCISES 


Introductory: 

A  long  while  ago  it  was  noticed  that  when  pure  water 
was  boiled  at  the  top  of  a  high  mountain,  it  was  not  so 
hot  as  when  pure  water  was  boiled  near  the  sea  level. 
This  is  because  the  pressure  of  the  air  is  less  at  the  moun- 
tain top.  The  boiling  point  of  pure  water,  under  standard 
conditions  of  barometric  pressure,  is  100°  C.  We  wish  to 
test  a  thermometer  to  determine  whether  its  100°  mark  is 
correctly  placed,  and  also  to  find  its  error,  if  any.  We 
shall  also  test  its  zero  graduation,  which  should  mark  the 
temperature  of  water  in  the  process  of  freezing,  or  of  ice 
in  the  process  of  melting. 

Experimental : 

Place  the  tabular  form  for  observations  near  the  top  of 

the  left-hand  page.  Record  all  readings  as  soon  as  made, 
(a)  Freezing  Point.  —  Fill  a  funnel  about 
half  full  of  cracked  ice  and  support  it  in  a 
jar  (Fig.  68).  Insert  the  thermometer  in 
such  a  way  that  the  ice  will  be  packed  around 
the  bulb  and  nearly  to  the  zero  of  the  scale. 

After  the  mercury  has  remained  stationary 
for  at  least  five  minutes,  take  the  reading  of 
the  thermometer  to  tenths  of  a  degree.  The 
difference  between  this  reading  and  the  zero 
of  the  scale  is  the  freezing  point  error  of  the 
instrument.  No  allowance  need  be  made  for 
the  atmospheric  pressure. 

State  the  correction  for  your  thermometer 
as  _  or  +,  according  as  the  freezing  point 
was  indicated  too  high  or  too  low.  This 
correction  should  be  added  algebraically  to 
all  readings  near  the  freezing  point  taken 

with  this  thermometer. 


Fig.  68. 


FIXED  POINTS  OF  A  THERMOMETER 


183 


(5)  Boiling  Point.  —  To  test  the  boiling  point  of  the 
thermometer,  see  that  the  chimney  is  on  the  boiler  and  the 
thermometer  adjusted  so  that  the  100°  mark  is  just  above 
the  stopper.  The  upper  tube  of  the  boiler  should  be 
open ;  the  lower  one  closed.  The  bulb  of  the  thermometer 
should  not  dip  into  the  water  in 
the  boiler,  which  is  half  filled 
with  water.  Boil  the  water  until 
the  reading  of  the  thermometer 
remains  stationary  for  at  least 
two  minutes.  Then  take  a  read- 
ing of  the  thermometer,  estimat- 
ing to  tenths  of  a  degree,  and 
record. 

(<?)  Next  determine  the  effect 
on  the  boiling  point  when  the 
pressure  is  increased.  To  the 
upper  side  tube  attach  the  bent 
glass  tube  so  that  it  points  down- 
ward. When  steam  is  escaping 


Fig.  69. 


vigorously,  immerse  the  long  glass  tube  in  a  jar  of  water, 
so  that  its  free  end  reaches  nearly  to  the  bottom  of  the  jar 
(Fig.  69).  Observe  the  temperature  when  the  mercury 
becomes  steady,  so  as  to  determine  the  effect  of  increased 
pressure  on  the  boiling  point. 

CAUTION.  As  soon  as  the  reading  has  been  made,  withdraw  the 
long  tube  from  the  jar  so  that  hot  water  rnay  not  crack  the  jar.  Turn 
out  the  flame  under  the  boiler. 

Calculation  of  the  True  Boiling  Point.  —  The  instructor 
will  give  you  at  this  point  the  barometer  reading  of  the 
day.  It  has  been  found  that  a  difference  of  a  millimeter 
in  pressure  makes  a  difference  of  0.037°  C.  in  the  boiling 
point.  T^hen  for  every  millimeter  of  the  barometer  read- 


184  LABORATORY   EXERCISES 

ing  in  excess  of  760  mm.,  add  0.037°  C.  to  100°  C.,  or  sub- 
tract 0.037°  C.  for  every  millimeter  of  barometer  pressure 
less  than  760  mm.  This  gives  the  true  boiling  point  of 
water  under  existing  barometric  conditions. 

The  difference  between  this  and  the  observed  boiling 
point  will  be  the  error  of  your  thermometer  at  the  boiling 
point.  State  the  correction  necessary  to  bring  your  ther- 
mometer to  the  true  boiling  point  as  +  or  — ,  according  as 
the  boiling  point  was  indicated  too  low  or  too  high.  This 
correction  is  added  algebraically  to  indicated  temperatures 
near  the  boiling  point  whenever  the  thermometer  is  used. 

OBSERVATIONS 

Number  of  thermometer 

Reading  in  melting  ice °  0. 

Reading  in  free  steam °  (7. 

Reading  in  steam  under  pressure       ....  °  C. 

Barometer  reading mm. 

Make  sectional  drawings  of  your  apparatus,  showing 
how  it  was  used.  Write  a  simple  description  of  how  you 
did  each  part  of  the  experiment. 

Place  the  table  of  calculated  results  at  the  top  of  the 
right-hand  page. 

CALCULATED  RESULTS 

True  boiling  point  for  to-day °  C. 

Boiling  point  error  of  the  thermometer  ...  °  C. 
Correction  for  thermometer  at  boiling  point 

(  +  or  -)  ....'. °  C. 

Freezing  point  error  of  thermometer  ...  °  C. 
Correction  for  thermometer  at  freezing  point 

(+  or  -)        °  C. 


PHENOMENA  OP  BOILING  185 

Discussion : 

What  is  the  general  effect  of  pressure  on  the  boiling 
point  ?  How  could  you  properly  graduate  a  finished  blank 
or  ungraduated  thermometer  ? 

Conclusion : 

The  corrections  for  thermometer  No. -are  °  C. 

(+<*•-) 

at  the  freezing  point,  and °  C.  at  the  boiling  point. 

(+  or  -) 


EXPERIMENT    52 

Phenomena  of  Boiling 

OBJECT.  To  observe  what  changes  occur  during  boiling  and 
the  effect  of  a  dissolved  substance  on  the  boiling  point. 

APPARATUS.  Distilling  flask,  150  cm.3;  ring  stand  with 
wire  gauze  supported  on  ring ;  small  clamp ;  perforated  flat  cork 
(!");  cork  stopper  to  fit  neck  of  flask  and  perforated  to  admit 
thermometer ;  beaker ;  elbow  tube  and  rubber  connections ;  ther- 
mometer reading  to  100°  C.;  Bunsen  burner ;  if  part  (d)  is  to  be 
done,  —  boiler  and  hydrometer  jar ;  short  pieces  of  glass  tubing  or 
rod. 

MATERIAL.     Coarse  salt, 

Introductory : 

Our  first  ideas  of  boiling  were  probably  obtained  from 
watching  the  teakettle  at  home.  We  knew  that  the  cover 
should  be  put  on  the  kettle  if  the  water  were  to  heat 
quickly.  We  have  seen  the  lid  rise  a  little  and  then  bump 
back,  until  finally  steam  issued  from  the  spout  and  a  sing- 
ing noise  was  heard. 


186 


LABORATORY   EXERCISES 


All  these  familiar  sights  and  sounds  are  the  phenomena 
of  boiling,  and  boiling  means  simply  the  disturbances  and 
changes  that  occur  during  the  transformation  of  a  liquid 
into  a.  gas.  In  a  glass  flask  all  these  phenomena  may  be 
readily  observed,  and  no  matter  how  many  times  we  may 
see  the  operations,  they  lose  none  of  their  first  fascination. 

Experimental : 

Arrange  the  apparatus  as  in  Fig.  70.  The  position  of 
the  cork  stopper  held  in  the  clamp  may  have  to  be  adjusted 
from  time  to  time  so  that  the  thermometer  scale  may  be 

read.  The  perforated  flat 
cork  is  slipped  over  the 
thermometer  and  then  ad- 
justed in  position  so  that 
it  forms  a  cap  resting  on 
the  top  of  the  neck  of  the 
flask.  The  thermometer 
should  slip  easily  through 
this  cork. 

Record  all  observations 
as  soon  as  made  in  a  tabu- 
lar form  near  the  top  of 
the  left-hand  page  (see 
page  188). 

(«)  Have  the  flask  a 
little  less  than  half  full 


I 


I 


Fig.  70. 


of  fresh  water.  Heat  the 
flask  with  a  small  flame, 
noting  where  bubbles  first  form,  the  size  of  the  bubbles, 
and  what  becomes  of  them  (Observation  1).  When  this 
first  bubbling  ceases,  remove  the  flame.  Slowly  lower  the 
thermometer  so  as  to  immerse  the  bulb  in  the  liquid. 
Note  the  temperature  (Observation  1).  Is  the  water  at 


PHENOMENA  OF  BOILING       •  187 

its  boiling  point  ?  What  makes  you  think  that  these  first 
bubbles  might  be  air  bubbles  ? 

Raise  the  thermometer  from  the  water  and  resume  the 
heating.  Note  where  the  bubbles  begin  to  form  after  a  time 
and  what  happens  to  them  as  they  proceed  toward  the  sur- 
face (Observations  2  and  3).  Take  the  temperature  of  the 
top  layer  of  water  (Observation  2) ;  also  the  temperature 
of  the  water  near  the  bottom  of  the  flask  (Observation  3). 
Explain  the  behavior  of  the  first  bubbles  in  this  second  heating. 

Raise  the  thermometer  so  that  its  bulb  stands  just  be- 
low the  opening  from  the  neck  to  the  delivery  tube  of  the 
flask.  Watch  the  formation  and  action  of  the  bubbles  as 
the  heating  continues,  increasing  the  flame  if  necessary 
(Observations  4,  5,  and  6).  When  steam  is  escaping 
freely  from  the  flask,  note  the  thermometer  reading  (Ob- 
servation 4).  Explain.  Then  take  the  temperature  of  the 
water  near  the  top  (Observation  5)  and  also  at  the  bottom 
of  the  flask  (Observation  6).  What  happens  to  the  steam 
passing  out  the  delivery  tube? 

In  case  your  flask  bumps  at  any  time  during  the  heating, 
see  what  happens  just  before  the  moment  of  the  bumping. 

(i)  Incline  the  distilling  flask,  and  let  two  short  pieces 
of  glass  tubing  or  glass  rod  slide  down  the  inside  of  "the 
neck.  Continue  the  heating,  noting  where  bubbles  form 
(Observation  7).  What  is  the  effect  on  the  rate  of  boil- 
ing ?  What  is  the  effect  of  introducing  the  glass  pieces  on 
the  amount  of  heated  surface  ? 

Glass  beads  are  often  used  to  prevent  bumping,  as  well 
as  to  save  time  in  laboratory  distillations. 

(c)  Remove  the  flask  from  the  flame,  and  after  inclin- 
ing it,  slide  in  about  a  dozen  pieces  of  coarse  salt.  Slowly 
add  water  until  the  flask  is  nearly  half  full  again  and, 
after  wiping  the  outside  dry,  replace  the  flask  on  the  gauze. 
Clamp  the  thermometer  so  that  its  bulb  is  immersed. 


188 


LABORATORY   EXERCISES 


Note  the  temperature  of  the  liquid  when  it  begins  to 
boil  freely1  (Observation  8).  Raise  the  thermometer  so 
as  to  take  the  temperature  of  the  vapor  (Observation  9). 
Taste  the  condensed  liquid  coming  from  the  delivery 
tube.  Is  it  salty? 

(d)  In  case  Part  (c)  of  Experiment  51  (page  183)  has 
not  been  performed,  determine  the  effect  on  the  boiling 
point  when  the  pressure  is  increased.  Arrange .  the  ap- 
paratus as  represented  in  Fig.  69  on  page  183.  Then  fol- 
low the  directions  given  in  the  first  paragraph  of  (c), 
on  that  page. 

CAUTION.  As  soon  as  the  reading  has  been  made,  withdraw  the 
long  tube  from  the  jar,  so  that  the  hot  water  may  not  crack  the  jar. 
Turn  out  the  flame  under  the  boiler. 

OBSERVATIONS 


NUMBER  OP 
OBSERVATION 


POSITION  OF 
THERMOMETER  BuLf 


TEMPERA- 
TURE 


WHERE  BUBBLES  FORM  AND 
TUEIR  BEIIAVIOB 


(a)  Water 
1 
2 
3 
4 

•      5 
6 

(6)  Pieces 
of  glass 

7 

(c)  Salt  solution 

8 

9 

(d)  Increased 


10 


1  Note  to  Instructor.  While  waiting  for  the  boiling  to  occur  in  Part 
(c),  the  students  should  be  directed  to  work  on  their  laboratory  note- 
books. 


PHENOMENA  OF  BOILING  189 

Make  a  drawing  of  your  apparatus.  Complete  the  de- 
scription of  how  the  experiment  was  done  by  statements 
supplementing  the  information  given  in  the  table  of  ob- 
servations. 

Discussion : 

Answer  under  this  heading  the  italicized  questions 
occurring  in  the  experimental  directions. 

What  change  of  state  occurs  in  the  vaporization  (boil- 
ing) of  a  liquid?  in  the  condensation  of  a  vapor? 

Conclusion : 

Complete  these  statements : 

., ,        f  smooth  ] 

A  liquid  boils  best  in  a  flask  with  a  j          .     1  surface. 

(rough    ) 

The  boiling  point  of  a  water  solution  is than  that  of 

pure  water.     The  boiling  point  is by  an  increase  of 

pressure. 


190  LABORATORY   EXERCISES 

EXPERIMENT    53 

• 

Coefficient  of  Linear  Expansion 

OBJECT.  To  determine  the  coefficient  of  linear  expansion  of  a 
given  material. 

APPARATUS.  Any  form  of  linear  expansion  apparatus,  the 
essentials  being:  a  tube  or  rod,  so  mounted  that  one  end  is 
clamped  firmly  and  the  other  is  free  to  move ;  if  a  rod  is  used, 
an  outer  tube  to  serve  as  a  steam  jacket ;  a  steam  boiler,  with 
rubber  tubing  to  connect  it  with  the  steam  jacket  or  tube  ;  Bunsen 
burner  ;  thermometer  ;  meter  stick  ;  lever  and  scale,  or  microm- 
eter screw,  for  magnifying  the  elongation.1 

Introductory : 

The  fact  that  bodies  expand  when  they  are 'heated  is 
very  familiar.  The  space  left  between  the  ends  of  the 
rails  on  a  railroad  is  designed  to  allow  for  the  difference 
in  length  in  winter  and  summer.  Although  the  propor- 
tional expansion  is  very  small,  the  total  change  in  length 
of  a  long  structure  may  be  considerable.  In  order  to  cal- 
culate the  total  elongation  of  any  body  when  heated,  it 
is  necessary  to  know  the  change  produced  in  a  unit  length 
by  a  change  in  temperature  of  one  degree.  This  increase 
in  length  per  unit  length  per  degree  Centigrade  is  called 
the  coefficient  of  linear  expansion  of  the  material.  As  the 

1  As  different  schools  are  supplied  with  different  forms  of  apparatus 
for  this  experiment,  it  was  not  considered  advisable  to  confine  the  experi- 
mental directions  to  any  one  form.  The  authors  would  recommend  to 
schools  making  their  own  apparatus  or  purchasing  new  apparatus,  that 
the  expansion  of  a  tube  rather  than  that  of  a  rod  be  measured,  as  this 
greatly  simplifies  the  apparatus.  If  the  tube  is  just  a  meter  long,  and 
the  magnifying  ratio  of  the  lever  or  screw  is  an  even  one,  as  1  to  20,  1  to 
50,  or  1  to  100,  calculations  will  be  greatly  simplified  and  the  pupil  will 
see  the  result  much  more  clearly. 


COEFFICIENT  OF  LINEAR  EXPANSION          191 

total  increase  in  length  of  such  a  specimen  as  can  be  used 
in  the  laboratory  is  very  small,  a  magnifying  lever,  having 
a  known  ratio  between  the  arms,  or  a  micrometer  screw, 
is  commonly  employed  to  make  possible  the  accurate  cal- 
culation of  the  total  elongation. 

Experimental : 

The  length  of  the  specimen  furnished  is  to  be  directly 
measured  in  centimeters  and  tenths  with  a  meter  stick. 
Care  should  be  taken  in  this  measurement  and  in  the  ad- 
justment of  the  apparatus  for  the  zero  reading,  to  handle 
the  specimen  as  little  as  possible,  so  that  its  initial  tem- 
perature may  remain  that  of  the  room.  This  temperature 
is  obtained  by  reading  a  thermometer  which  has  been  in 
contact  with  or  very  close  to  the  specimen  for  some  time. 

The  specimen  is  then  mounted  as  directed  by  the  in- 
structor, care  being  taken  that  it  is  free  to  move  only  at 
the  end  provided  with  the  device  for  obtaining  tfce  amount 
of  elongation.  The  position  of  the  pointer,  or  the  microm- 
eter head,  at  the  room  temperature  is  then  observed  to 
tenths  of  the  smallest  division,  and  recorded.  The  room 
temperature  is  also  recorded. 

Steam  is  next  passed  through  the  tube,  or  through  the 
jacket  surrounding  the  rod,  for  at  least  ten  minutes.  If 
a  steam  jacketed  rod  is  used,  the  temperature  of  the  rod 
may  be  taken  as  that  of  a  thermometer  whose,  bulb  is 
inside  the  jacket  in  contact  with  the  rod.  If  a  tube  is 
used,  through  which  the  steam  directly  passes,  the  tem- 
perature may  be  taken  as  the  boiling  point  of  the  day, 
which  will  be  furnished  by  the  instructor. 

With  the  lever  form  of  apparatus,  it  is  only  necessary 
to  take  the  final  reading  of  the  pointer  and  determine  the 
ratio  of  the  lever  arms.  When  a  micrometer  is  used,  the 
screw  should  be  turned  back  from  the  end  of  the  rod  im- 


192  LABORATORY   EXERCISES 

mediately  after  taking  the  reading  at  room  temperature, 
and,  after  the  tube  has  reached  the  temperature  of  the 
steam,  the  screw  is  again  brought  in  contact  with  the  end 
of  the  tube  and  the  reading  taken  and  recorded.  Steam 
should  be  passing  freely  when  the  final  readings  are 
taken. 

As  soon  as  the  readings  have  been  taken,  the  steam 
supply  should  be  discontinued,  so  that  the  specimen  may 
cool  to  room  temperature  as  rapidly  as  possible,  and  so  be 
ready  for  a  repetition  of  the  experiment  if  necessary. 

All  readings  taken  directly  from  the  apparatus  are  to 
be  recorded  in  tabular  form  near  the  top  of  the  left-hand 
page. 

OBSERVATIONS 

Initial  length cm. 

Initial  scale  reading cm. 

Final  scale  reading cm. 

Ratio  of  lever  arms 

Room  temperature °  O. 

Steam  temperature °  '(7. 

Make  a  simple  outline  drawing  of  the  apparatus,  and 
write  a  brief  description  of  the  method  employed  in  the 
experiment. 

From  the  readings  obtained,  the  total  elongation,  the 
change  in  temperature,  and  the  expansion  in  centimeters 
per  degree  Centigrade  per  centimeter  can  be  obtained 
by  calculation.  The  results  should  be  entered  in  tabular 
form  at  the  top  of  the  right-hand  page. 

CALCULATED  RESULTS 

Difference  in  scale  readings cm. 

Total  expansion cm. 


COEFFICIENT  OF  CUBICAL  EXPANSION         193 

Difference  in  temperature °  C. 

Expansion  per  degree  C. cm. 

Expansion  per  degree  C.  per  centimeter  (linear 
coefficient) 

Discussion  : 

Explain  the  method  of  calculating  the  actual  expansion 
from  the  scale  readings,  if  the  lever  apparatus  was  used. 

If  the  micrometer  apparatus  was  used,  explain  the 
method  of  obtaining  readings  with  the  micrometer. 

Conclusion : 

The  coefficient  of  linear  expansion  of is 


EXPERIMENT    54 

Coefficient  of  Cubical  Expansion 

OBJECT.  To  determine  the  coefficient  of  cubical  expansion  of 
mercury,  relative  to  glass. 

APPARATUS.  Specific  gravity  bottle,  25  cm.3,  having  a  stopper 
with  a  capillary  hole  ; l  ring  stand  with  one  ring  and  wire  gauze  ; 
thermometer ;  pipe-stem  triangle,  with  the  wire  ends  doubled 
under ;  beaker  large  enough  to  permit  the  bottle,  resting  on  the 
triangle,  to  be  immersed  to  a  point  above  the  bottom  of  the  stopper  ; 
Bunsen  burner ;  balance  ;  weights  ;  one  funnel  for  the  class,  as 
described  in  footnote  on  page  194. 

MATERIAL.     Mercury. 

Introductory : 

The  tubes  of  alcohol  thermometers  are  larger  than  those 
of  mercury  thermometers,  because  alcohol  has  a  greater 

1  The  use  of  the  specific  gravity  bottle  in  this  experiment  was  suggested 
by  Mr.  Charles  H.  Slater. 


194  LABORATORY  EXERCISES 

rate  of  expansion  than  mercury.  Both  alcohol  and  mer- 
cury expand  more  than  glass ;  otherwise  the  expansion  of 
the  glass  bulb  and  stem  would  cause  the  liquid  column  in 
the  stem  to  fall  instead  of  rise.  Since  mercury  is  often 
contained  in  glass  vessels,  as  in  the  thermometer,  barome- 
ter, and  other  pieces  of  apparatus,  it  is  important  to  know 
the  relative  rate  of  expansion  of  the  two. 

A  bottle  completely  filled  with  a  known  weight  of  mer- 
cury is  heated  through  a  measured  change  of  temperature, 
and  the  weight  of  the  mercury  which  overflows  is  found. 
As  weights  of  the  same  substance  are  proportional  to  the 
corresponding  volumes,  it  is  easy  to  calculate  the  propor- 
tion of  the  original  volume  by  which  the  mercury  expands 
for  each  unit  change  of  temperature.  This  quantity  is 
the  coefficient  of  cubical  expansion  of  mercury.  As  the  glass 
bottle  has  been  heated  to  the  same  temperature  as  the 
mercury,  the  expansion  measured  is  relative  to  the  expan- 
sion of  the  glass,  and  so  the  coefficient  obtained  is  relative 
to  glass. 

Experimental : 

A  specific  gravity  bottle,  having  a  perforated  stopper, 
is  filled  with  mercury  under  the  direction  of  the  instructor.1 
Care  must  be  taken  in  filling  to  see  that  no  air  is  left 
under  the  stopper  and  that  the  capillary  tube  in  the  stop- 
per is  completely  filled.  The  bottle  should  be  handled  by 
the  neck,  -to  prevent  the  heat  of  the  hand  from  forcing 

1(The  mercury  may  well  be  contained  in  a  funnel,  having  a  jet  tube 
attached  by  soft  rubber  tubing,  with  a  screw  compressor  on  the  tubing. 
A  porcelain  dish  is  placed  beneath  it  to  catch  the  overflow.  At  the  close 
of  the  experiment,  the  pupils  may  pour  off  most  of  the  water  from  their 
beakers,  and  then  pour  the  mercury  and  remaining  water  back  into  the 
funnel.  The  separation  of  water  from  mercury  will  then  be  compara- 
tively easy. 


COEFFICIENT  OF  CUBICAL  EXPANSION         195 


any  mercury  out.  The  bottle  and  its  contents  are  then 
weighed  at  room  temperature,  and  both  weight  and  tem- 
perature recorded  in  tabular  form  near  the  top  of  the  left- 
hand  page. 

The  bottle  is  next  placed  on  a  pipe-stem  triangle,  in  a 
beaker  on  a  ring  stand,  and  water  added  until  it  has 
reached  the  level  of  the  bottom  of 
the  stopper  in  the  bottle  (Fig.  71). 
The  water  is  heated  with  a  Bunsen 
burner  until  it  boils,  and  kept  at  a 
boiling  temperature  for  5  minutes. 
While  it  is  boiling,  the  temperature 
of  the  water  is  taken  with  a  ther- 
mometer and  recorded.  Observe 
what  happens  to  the  mercury  in 
the  bottle. 

The  beaker  is  now  removed  from 
the  ring  stand.  By  dipping  out 
hot  water  and  adding  cold  water, 
the  temperature  of  the  water  is 
brought  approximately  to  that  of 
the  room.  Care  must  be  taken 
during  this  operation  to  avoid  get-  Fi  ^j 

ting   any   water    into    the    specific 

gravity  bottle.  The  bottle  is  now  removed  from  the 
water,  carefully  dried,  and  again  weighed. 

After  being  weighed,  the  bottle  is  returned  to  the 
instructor,  still  containing  the  mercury.  The  greater 
part  of  the  water  in  the  beaker  is  to  be  poured  off,  with- 
out losing  any  mercury.  The  remaining  water  arid  mer- 
cury is  to  be  disposed  of  as  the  instructor  may  direct. 

The  readings  taken  should  be  entered  in  a  tabular  form 
near  the  top  of  the  left-hand  page. 


196  LABORATORY   EXERCISES 

OBSERVATIONS 

Weight  of  empty  bottle g. 

Weight  of  bottle  filled  with  mercury,  initial  .     .  g. 

Weight  of  bottle  with  mercury,  final     ....  g. 

Initial  (room)  temperature °  C. 

Final  (boiling}  temperature °C. 

A  simple  drawing  of  the  apparatus  and  a  brief  descrip- 
tion of  the  operations  in  the  experiment  should  follow  the 
table  of  observations  on  the  left-hand  page. 

At  the  top  of  the  right-hand  page,  place  the  following 
table  of  calculated  results,  making  the  required  computa- 
tions on  the  page  immediately  beneath  the  table. 

CALCULATED  RESULTS 

Jnitial  weight  of  mercury  (<z) g. 

Weight  of  mercury  lost  by  expansion  (6)      .     .         g. 
Change  in  temperature  (c) °(7. 

Loss  by  expansion  per  degree  (d  =  -\      ...         g. 
Coefficient  of  cubical  expansion  ( - 

Discussion : 

Explain  clearly  how  the  loss  in  weight  per  degree, 
divided  by  the  original  weight,  gives  the  coefficient  of 
cubical  expansion. 

Conclusion : 

The  coefficient  of  cubical  expansion  of  mercury  relative 
to  glass  is . 


INCREASE  IN  VOLUME  AT  CONSTANT  PRESSURE      197 
EXPERIMENT    55 

Increase  in  Volume  at  Constant  Pressure 

OBJECT.  To  find  the  relation  between  the  increase  in  the  volume 
of  a  gas  and  the  increase  in  temperature  causing  the  change,  when 
the  pressure  remains  constant. 

APPARATUS.  Steam  boiler  with  chimney,  having  the  lower 
side  outlet  closed  with  a  rubber  tube  and  a  screw  compressor ; 
Charles'  law  tube,  Waterman  form ;  thick  cardboard  square, 
3"  x  3",  perforated  to  admit  Charles'  law  tube ;  narrow  jar  or 
cylinder  about  8"  high ;  thermometer ;  ring  stand  and  clamp ; 
Bunsen  burner. 

MATERIAL.     Finely  cracked  ice,  or  snow. 

Introductory : 

The  expansion  of  solids  by  heat  is  a  familiar  fact.  The 
rate  at  which  metals  expand  for  each  degree  of  tempera- 
ture has  been  carefully  studied.  It  has  been  found  that 
each  metal  has  its  characteristic  rate  (coefficient  of  ex- 
pansion). With  gases,  however,  the  rate  is  the  same  for 
them  all,  but  its  determination  is  made  more  difficult  by 
the  fact  that  the  volume  of  a  gas  is  also  affected  by  atmos- 
pheric pressure.  The  effect  of  this  pressure  in  the  ex- 
pansion of  solids  is  so  slight  that  it  is  disregarded  in  the 
determination  of  their  coefficient  of  expansion. 

As  the  atmospheric  pressure  seldom  varies  much  in  a 
short  time,  the  effect  of  an  increase  of  temperature  on  the 
volume  of  a  gas  is  found  by  measuring  the  volume  at  two 
different  temperatures  and  under  atmospheric  pressure. 
The  two  most  convenient  temperatures  for  the  determina- 
tion are  0°C.  and  100°  C.,  respectively,  as  these  tempera- 
tures are  easy  to  obtain  with  ioe  and  etearn.  The  gas  is 
confined  in  a  Charles'  law  tube  by  means  of  a  mercury 


198 


LABORATORY   EXERCISES 


plug,  which  is  free  to  move  as  the  volume   of   the   gas 
changes. 

The  relation  between  volume  and  temperature  under 
constant  pressure  is  most  conveniently  expressed  with 
reference  to  the  absolute  scale  of  temperature.  On  this 
scale  the  zero  corresponds  to  —  273°  C.  The  Centigrade 
zero  is  equivalent  to  273°  A.  To  change  Centigrade 
temperatures  to  absolute  temperatures,  add  273°  algebrai- 
cally. 

Experimental : 

With  the  steam  boiler  half  full  of  water,  light  the 
burner  underneath,  and  screw  on  the  chimney.  The 
lower  outlet  for  the  escape  of  steam  should  be  closed  by  a 

screw  compressor 
on  a  rubber  tube. 
While  waiting  for 
the  water  to  boil, 
determine  the  vol- 
ume of  inclosed  air 
at  0°  C.  as  directed 
in  (a). 

(a)  The  mer- 
cury index  in  the 
Charles'  law  tube 
should  stand  at 
about  the  center  of 
the  graduated  scale. 
Insert  the  tube, 


Fig.  72. 


with  its  scale,  in  a  jar  containing  finely  cracked  ice, 
or  snow,  so  that  the  mercury  index  is  a  short  distance 
above  the  surface  of  the  ice.  Note  the  descent  of  the 
index  as  the  inclosed  air  contracts.  When  no.  further 
contraction  occurs  and  the  inclosed  air  is  all  surrounded 


INCREASE  IN  VOLUME  AT  CONSTANT  PRESSURE      199 

by  melting  ice  (Fig.  72,  B),  take  the  reading  of  the  index 
on  the  graduated  scale.  Since  the  tube  is  of  uniform 
diameter,  the  length  of  the  inclosed  column  of  air  may  be 
taken  as  the  measure  of  its  volume.  Record  the  reading 
in  a  tabular  form  near  the  top  of  the  left-hand  page. 

(i)  Remove  the  air  tube  from  the  ice,  and  allow  it  to 
stand  five  minutes  or  so  in  the  air  to  regain  the  room 
temperature.  Then  slowly  slip  the  tube  with  its  scale 
through  the  cardboard  cover  on  top  of  the  chimney  of  the 
boiler.  The  mercury  index  should  be  just  visible  above 
the  cardboard  (Fig.  72,  (7).  When  the  column  of  in- 
closed air  has  been  brought  to  the  temperature  of  the 
steam,  the  index  will  become  stationary.  Clamp  the  tube 
in  this  position,  with  the  index  just  above  the  cardboard, 
then  read  and  record  the  position  of  the  index  on  the  scale. 
Remove  the  tube  from  the  boiler. 

Insert  the  bulb  of  a  thermometer  in  the  steam  within 
the  chimney.  When  the  mercury  becomes  stationary, 
read  and  record  the  temperature. 

OBSERVATIONS 

Length  (volume)  of  inclosed  air  at  0°  O.     .     .  cm. 
Length  (volume)  of  inclosed  air  at  steam 

temperature cm. 

Temperature  of  the  steam °  C. 

Make  simple  drawings,  showing  the  Charles'  law  tube 
in  position  at  each  of  the  two  temperatures.  Briefly  d§- 
scribe  the  experimental  method. 

Change  the  Centigrade  temperatures  to  absolute  tem- 
peratures, and  record  in  a  table  of  calculated  results  placed 
at  the  top  of  the  right-hand  page. 

Find  (a)  the  increase  in  volume  of  the  air  ;  (6)  the 
fraction  of  the  original  volume  which  this  increase  is, 


200  LABORATORY   EXERCISES 

expressing  the  result  to  three  decimal  places  ;  (c)  the 
fractional  (decimal)  increase  in  temperature  over  the  initial 
absolute  temperature.  Record  these  in  the  table. 

CALCULATED  RESULTS 

0°  Centigrade        °  absolute 

°  Centigrade °  absolute 

Increase  in  length  (volume}  of  inclosed 

air cm. 

Fractional  increase  in  volume  .    = 

Fractional  increase  in  temperature = 

Discussion : 

Why  was  the  inclosed  gas  regarded  as  being  under 
constant  pressure  ?  Compare  the  two  decimals  represent- 
ing the  fractional  increases  in  volume  and  in  temperature 
(absolute  scale).  What  would  be  the  fractional  increase 
in  volume  for  one  degree?  for  twenty  degrees?  What 
would  be  the  fractional  decrease  in  volume  when  the  gas 
was  cooled  ten  degrees  ?  In  each  case  assume  the  original 
temperature  to  be  0°  C. 

Conclusion : 

Complete  this  statement: 

Under  constant  pressure,  the  volume  of  a  gas  is. to 

its  temperature  on  the scale. 


INCREASE  IN  PRESSURE  AT  CONSTANT  VOLUME      201 
EXPERIMENT    56 

Increase  in  Pressure  at  Constant  Volume 

OBJECT.  To  find  the  relation  between  the  increase  in  pressure 
of  a  gas  and  the  increase  in  temperature  causing  this  change,  when 
the  volume  of  the  gas  remains  constant. 

APPARATUS.  Charles'  law  tube  (Hall  and  Bergen  form) ; 
glass  condenser  with  inner  tube  removed  ;  1-hole  cork  stopper  to 
fit  opening  at  one  end  of  condenser  tube  and  solid  cork  for  other 
end  ;  ring  stand  with  condenser  clamp ;  ring  stand  with  small 
clamp  for  raising  free  end  of  Charles'  law  tube ;  steam  boiler  with 
cap  ;  rubber  tubing  to  connect  steam  boiler  with  condenser  tube  ; 
tubulated  ice  tray  with  1-hole  cork  to  fit ;  burner;  meter  stick; 
beaker. 

MATERIAL.     Cracked  ice,  or  snow. 

Introductory : 

If  a  hot  fire  is  maintained  under  a  steam  boiler  when 
the  engine  is  not  running,  the  steam  pressure  increases 
and,  if  it  were  not  for  the  safety  valve,  the  boiler  would 
burst.  When  a  tea  kettle  begins  to  boil,  the  pressure  of 
the  steam  lifts  the  lid.  In  both  of  these  cases  a  gas, 
steam,  is  heated  in  such  a  way  as  to  prevent  it  from 
expanding.  In  our  experiment,  a  certain  amount  of  air 
will  be  confined  in  a  tube  at  the  temperature  of  melting 
ice ;  it  will  then  be  heated  to  the  temperature  of  steam, 
but  its  volume  will  be  kept  the  same  by  increasing  the 
pressure  upon  it.  From  our  results  we  may  reach  a  con- 
clusion regarding  the  relation  between  the  temperature  of 
a  gas  and  its  pressure,  when  the  volume  is  kept  constant. 
The  Centigrade  temperatures  given  by  our  thermometer 
will  be  changed  to  absolute  temperatures  by  adding  273° 
algebraically  to  the  Centigrade  reading. 


202  LABORATORY   EXERCISES 

Experimental : 

CAUTION.  Do  not  allow  the  open  end  of  the  Charles'  law  tube  to 
get  below  the  horizontal  position,  or  the  mercury  may  run  out. 

See  that  the  steam  boiler  is  half  full  of  water,  the  cap 
in  place,  and  the  steam  outlet  at  the  side  open.  Connect 
with  rubber  tubing  the  steam  outlet  of  the  boiler  with  the 
steam  inlet  of  the  steam  jacket  (condenser  tube).  Place 
a  beaker  beneath  the  outlet  tube  of  the  condenser,  Fig.  74, 
to  catch  any  condensed  steam.  Light  the  burner  under 


1 


Fig.  73. 

the  boiler,  so  that  there  will  be  a  supply  of  steam  ready 
for  the  steam  jacket. 

(a)  Pass  the  closed  end  of  the  air  tube  through  the 
cork  of  the  ice  tray  and  cover  this  portion  of  the  tube 
with  finely  cracked  ice.  When  the  inclosed  air  column 
no  longer  contracts,  adjust  the  position  of  the  tube  in  the 
stopper,  so  that  the  mercury  in  the  tube  extends  just  to 
the  outer  end  of  the  stopper  ((7,  Fig.  73).  The  other 
end  of  the  mercury  column  should  be  at  the  same  height 
above  the  table  top  as  the  mercury  at  (7,  so  that  the 
volume,  CD,  of  inclosed  air  will  be  at  atmospheric  pressure. 
The  necessary  elevation  may  be  obtained  by  the  use  of  a 
small  piece  of  glass  tubing  (6r,  Fig.  73). 

Measure  the  distance  from  C  to  B,  the  nearer  end  of  the 
rubber  connection,  and  record  in  the  table  of  observations 
near  the  top  of  the  left-hand  page. 

(6)  Remove  the  air  tube  with  its  stopper  from  the  ice 
tray,  and  fit  it  into  the  steam  jacket  (Fig.  74)  so  that  the 
distance  BO  is  just  the  same  as  with  the  ice  tray. 


INCREASE  IN  PRESSURE  AT  CONSTANT  VOLUME      203 

Support  the  outer  end  of  the  air  tube  in  a  movable 
clamp  on  a  vertical  support.  As  the  air  in  the  tube 
expands,  keep-  raising  the  level  of  the  outer  tube  (JJ5, 
Fig.  74),  so  that  the  inner  end  of  the  mercury  column 
extends  just  to  O.  By  this  means  the  volume  of  the 
inclosed  air  is  kept  the  same  as  the  volume  of  the  air 
which  was  measured  at  0°  C. 

In  order  to  keep  this  volume  of  air  constant,  it  has  been 
necessary  to  increase  the  pressure  upori  it  by  raising  a 


Fig.  74. 


portion  of  the  mercury  column.  The  increase  in  pressure, 
in  millimeters  of  mercury,  is  the  difference  between  the 
height  of  the  outer  and  the  inner  ends  of  the  mercury 
column.  Determine  these  vertical  distances  above  the 
table  top  and  record  them  in  the  table.  Also  read  the 
barometer  and  record  the  reading. 

OBSERVATIONS 


Part  (a)  Temperature  0°  0.  (melting  ice) 

Length  BC 

Pressure  of  inclosed  air  (Barometer  reading) 

Part  (5)  Barometer  reading 

Height  of  outer  end  of  mercury  above  table  top 
Height  of  inner  end  of  mercury  above  table  top 


mm. 


mm. 


204  LABORATORY  EXERCISES 

Make  simple  drawings,  showing  the  arrangement  of  the 
air  tube  at  each  of  the  two  temperatures.  Briefly  describe 
the  experimental  method,  with  particular  reference  to  the 
means  of  keeping  the  volume  constant. 

Calculate  the  boiling  point  of  water  (temperature  of 
steam)  at  the  observed  barometric  pressure.  This  is  done 
by  adding  to  100°  C.,  0.037°  for  each  millimeter  of  baro- 
metric pressure  above  760  mm.,  or  subtracting  the  same 
amount  from  100°  C.  for  each  millimeter  below  760  mm. 
Record  this  temperature  of  steam  in  a  table  of  calculated 
results  at  the  top  of  the  right-hand  page.  Change  the 
two  Centigrade  temperatures  to  the  corresponding  absolute 
temperatures,  by  adding  273°,  and  record. 

Calculate  (a)  the  increase  in  absolute  temperature ; 
(6)  the  increase  in  pressure ;  (c)  the  total  pressure  of  the 
inclosed  air  at  the  temperature  of  steam  ;'  (rf)  the  decimal 
fraction  (three  places)  which  the  increase  in  pressure  is  of 
the  initial  (atmospheric)  pressure;  the  fractional  increase 
in  temperature  over  the  initial  temperature,  using  absolute 
degrees,  expressed  as  a  decimal  (three  places). 

CALCULATED  RESULTS 

0°  Centigrade      .     .     .     ....**.     °  absolute 

°  Centigrade  (temperature  of 

steam} =  °  absolute 

Increase  in  absolute  temperature  of 

inclosed  air °  absolute 

Increase  in  pressure  of  inclosed  air  mm. 

Total  pressure  of  inclosed  air  at 
steam  temperature mm. 

Fractional  increase  in  pressure  of  air 

Fractional  increase  in  absolute  tem- 
perature of  air 


LAW  OF  HEAT  EXCHANGE  205 

Discussion : 

Compare  the  fractional  increase  in  pressure  with  the 
fractional  increase  in  absolute  temperature.  How  much 
was  the  increase  in  pressure  for  each  degree  absolute  ? 

Conclusion : 

Complete  this  statement : 

When  the  volume  of  a  gas  is  kept  constant,  the  pressure 
of  the  gas  is to  its  temperature  on  the scale. 


EXPERIMENT    57 

Law  of  Heat  Exchange 

OBJECT.  To  find  the  relation  between  the  heat  lost  by  a  hot 
body  and  the  heat  gained  by  a  cold  body,  when  the  two  are  brought 
in  contact. 

APPARATUS.  Boiler,  with  dipper  to  fit ;  calorimeter ;  small 
battery  jar;  perforated  cardboard  square;  graduate  (100  cm.3); 
flask  (250  cm.3),  with  1-hole  rubber  stopper  to  fit ;  2  thermome- 
ters ;  Bunsen  burner ;  balance  ;  metric  weights ;  an  ice  shaver 
(Fig.  75)  is  convenient. 

MATERIAL.  Shaved  ice  or  snow  in  covered  crock;  several 
pailfuls  of  hot  water ;  cotton  batting. 

Introductory : 

When  cream  is  poured  into  hot  coffee,  the  mixture  be- 
comes cooler  than  the  coffee  and  warmer  than  the  cream. 
A  tub  of  hot  water  apparently  loses  heat  when  cold  water 
is  run  into  it.  What  really  happens  is  the  gaining  of  heat 
by  the  cold  water  at  the  expense  of  the  hot  water.  Does 
such  a  transfer  of  heat  take  place  according  to  any  fixed 
principle  ?  This  question  may  be  answered  by  mixing 


206  LABORATORY  EXERCISES 

weighed  amounts  of  hot  and  cold  water,  each  of  known 
temperature,  and  taking  the  temperature  of  the  mixture. 

In  order  to  make  the  calculations  required  to  establish 
the  law  of  heat  exchange,  it  is  necessary  to  define  a  unit 
of  heat  measurement,  called  the  calorie.  This  is  the 
amount  of  heat  which  will  raise  the  temperature  of  one 
gram  of  water  one  degree  Centigrade. 

Experimental : 

Handle  the  thermometers  carefully,  as  the  glass  forming  the  bulb 
is  very  thin.  Do  not  pour  hot  water  on  a  cold  thermometer,  nor 
cold  water  on  a  hot  thermometer.  Keep  your  note-book  close  at 
hand,  so  as  to  record  the  temperatures  as  soon  as  read.  Read  all 
temperatures  to  tenths  of  a  degree. 

Measure  with  a  graduate  200  cm.3  of  water  into  the 
dipper  of  the  steam  boiler.  See  that  the  boiler  is  about 
half  full  of  water  and  then  light  the  burner  beneath  it. 
While  waiting  for  the  water  to  heat,  do  Part  (a). 

(a)  Weigh  the  calorimeter  empty  and  dry.  Put 
shaved  ice,  or  snow,  into  a  graduate  up  to  the  15  cm.3 

mark  and  then  add  water 
to  the  100  cm.3  mark.  Pour 
the  mixture  into  the  cal- 
orimeter and  weigh  again. 
Keep  the  outside  of  the  cal- 
orimeter wiped  dry  during 

Fig.  75.     Ice  Shaver.  F  J  8 

the    weighing.       Place   the 

calorimeter  in  a  battery  jar,  rilling  the  space  between  the 
two  with  cotton  wool  or  other  non-conducting  packing. 
Cover  the  top  of  the  calorimeter  with  a  cardboard  square, 
having  a  hole  in  the  center,  through  which  a  thermometer 
is  inserted. 

Measure  100  cm.3  of  water  into  an  Erlenmeyer  flask 
fitted  with  a  1-hole  rubber  stopper,  carrying  a  ther- 


LAW  OF  HEAT  EXCHANGE  207 

mometer  adjusted  so  that  the  bulb  is  near  the  bottom  of 
the  flask  when  the  stopper  is  in  place. 

Warm  the  water  in  the  flask  by  dipping  the  flask  into  a 
pail  of  hot  water.  A  slight  rotary  motion  given  to  the 
flask  will  insure  uniform  heating.  The  water  is  to  be 
heated  to  as  many  degrees  above  the  room  temperature 
(which  will  be  placed  on  the  blackboard)  as  the  tempera- 
ture of  the  water  in  the  calorimeter  is  below  the  room 
temperature.  Read  and  record  promptly  the  temperatures 
of  the  two  masses  of  water. 

Then  lift  off  the  cardboard  cover  from  the  thermometer 
in  the  calorimeter.  Pour  the  warm  water  from  the  flask 
into  the  calorimeter,  letting  it  run  down  the  thermometer 
which  was  used  in  the  flask.  For  about  half  a  minute 
stir  the  mixture  of  warm  and  cold  water,  using  both 
thermometers  with  the  bulbs  held  together.  Read  and 
record  the  average  reading  of  the  two  thermometers. 

Touch  the  bulbs  of  the  thermometers  to  the  side  of  the 
calorimeter  to  remove  any  adhering  water,  and  take  them 
out  of  the  vessel.  Weigh  the  calorimeter  and  its  contents, 
and  record. 

Place  one  of  the  thermometers  in  the  water  in  the  calo- 
rimeter and  keep  it  for  Part  (6),  as  this  is  the  mass  of  cold 
water  to  be  used  in  that  part  of  the  experiment. 

(6)  By  this  time  the  water  in  the  dipper  will  probably 
be  hot.  Carefully  introduce  a  thermometer  and  stir  until 
the  temperature  of  the  water  is  ascertained.  Record  this 
at  once.  Then  quickly  read  and  record  the  temperature 
of  the  water  in  the  calorimeter. 

Pour  the  water  from  the  dipper  into  the  calorimeter, 
and  stir  with  the  two  thermometers  for  about  half  a  min- 
ute. Read  and  record  the  average  reading  of  the  two 
thermometers.  Weigh  the  calorimeter  and  the  mixture. 
Record. 


208  LABORATORY   EXERCISES 

OBSERVATIONS 

PART  (a)  PART  (6) 

Weight  of  calorimeter  empty  .  .  g. g. 

Weight  of  calorimeter  and  cold 

water g. g. 

Weight  of  calorimeter  and  mixture  g. g. 

Temperature  of  cold  water  .  .  °  C. °  C. 

Temperature  of  warm  (or  hot) 

water °  O. °  O. 

Temperature  of  mixture  .  .  .  °  C. °  O. 

Temperature  of  room  ....  -°  C. .°  C. 

Describe  briefly  the  essential  operations  in  each  part  of 
the  experiment.  Make  a  sectional  drawing  of  the  calo- 
rimeter and  battery  jar,  showing  how  the  calorimeter  was 
protected  from  loss  or  gain  of  heat  from  without. 

Calculate  in  both  parts  of  the  experiment  the  calories 
(1)  lost  by  the  warm  (or  hot)  water,  (2)  gained  by  the 
cold  water.  The  weights  of  water  mixed  can  be  found 
from  the  weights  recorded.  The  temperature  of  the  room 
is  not  to  be  considered  in  the  calculations.  Record  the 
results  in  tabular  form  at  the  top  of  the  right-hand  page. 

CALCULATED  RESULTS 

PART  (a)  PART  (b) 

Weight  of  cold  water        .     .     .  g.      g. 

Weight  of  warm  (or  hot)  water  g.     g. 

Fall   in   temperature   of   warm 

water °  C.     °  (7. 

Rise    in    temperature    of   cold 

water _°  C.     °  C. 

Calories  of  heat  lost  I y  hot  water  col.  col. 

Calories  of  heat  gained  by  cold 

water ..   col.  _.     ..  col. 


SPECIFIC  HEAT  OF  A  METAL  209 

Discussion : 

Define  a  calorie.  If  there  was  an  inequality  in  the  calo- 
ries of  heat  lost  and  gained,  some  heat  must  have  been 
wasted.  Could  the  calorimeter,  the  thermometers,  or  the 
air  account  for  heat  wasted?  Explain.  Why  is  it  desir- 
able to  have  the  temperature  of  the  mixture  the  same  as  the 
room  temperature?  Which  part  of  the  experiment  should 
give  you  the  closer  agreement  in  its  results?  Why? 

Conclusion : 

Complete  the  following  statement : 

The  number  of  calories  of  heat  lost  by  a  hot  body  equals 


EXPERIMENT    58 

Specific  Heat  of  a  Metal 

OBJECT.  To  find  the  specific  heat  of  lead  by  the  method  of  mix- 
tures.1 

APPARATUS.  Lead  cylinder  with  conical  top,  weighing  about 
600  g.  to  700  g.,  having  a  stout  linen  thread  for  suspension; 
spring  balance  (2000  g.)  ;  boiler;  Bunsen  burner;  ther- 
mometer ;  graduate  ;  calorimeter. 

Introductory : 

An  empty  tea  kettle,  placed  on  the  stove,  soon  reaches  a 
temperature  equal  to  that  of  boiling  water.  If,  however, 
a  weight  of  water  be  poured  into  the  kettle  equal  to  its 
own  weight,  it  will  take  several  times  as  long  to  bring  the 
water  to  the  boiling  temperature.  That  is,  more  heat  is 

1  Iron  or  aluminum  may  be  used  in  place  of  lead,  if  the  instructor  pre- 
fers ;  the  lead  cylinders,  however,  can  be  easily  cast,  and  the  use  of  a 
single  solid  piece  of  metal  is  dysidedly  preferable  to  shot. 


210 


LABORATORY  EXERCISES 


required  to  heat  one  pound  or  one  gram  of  water  one 
degree  than  is  required  to  heat  one  pound  or  one  gram  of 
iron  one  degree.  No  other  solid  or  liquid  requires  as  much 
heat  to  raise  one  gram  of  it  one  degree  as  water  requires 
for  the  same  change  ;  the  other  substances  absorb  or  give 
out  less  than  one  calorie  per  gram  per  degree.  The  fraction 
of  a  calorie  absorbed  or  given  out  wjien  one  gram  of  a  sub- 


Fig.  76. 

stance  changes  temperature  through  one  degree,  is  called 
the  specific  heat  of  the  substance. 

By  heating  a  weighed  piece  of  lead  to  the  temperature 
of  boiling  water  and  then  cooling  it  in  a  known  weight  of 
water  at  a  certain  temperature,  the  calories  given  to  the 
cold  water  by  the  hot  lead  can  be  calculated,  and  also  the 
calories  yielded  by  each  gram  of  lead  for  each  degree 
change  in  its  temperature. 

Experimental: 

Fill  the  boiler  half  full  of  cold  water  and  light  the 
burner  underneath  it.  Weigh  th#  lead  cylinder  (Fig-  76, 


SPECIFIC  HEAT  OF  A  METAL  211 

A~)  and  record  its  weight  in  a  table  of  observations  placed 
near  the  top  of  the  left-hand  page.  Place  the  cylinder  in 
the  boiler,  and  allow  it  to  remain  there  for  five  minutes 
after  the  water  begins  to  boil  freely. 

While  the  lead  is  being  heated,  measure  out  into  the 
calorimeter  300  cm.3  of  cold  water  from  the  tap.  Record 
the' weight  of  water  taken,  considering  1  cm.3  equivalent 
to  a  gram. 

When  the  lead  has  reached  the  temperature  of  the  boil- 
ing water,  read  and  record  the  temperature  of  the  cold 
water.  Quickly  raise  the  lead  with  the  thread,  touching 
it  to  the  edge  of  the  boiler  as  it  is  taken  out  so  as  to  dis- 
lodge any  drops  of  water,  and  place  the  lead  in  the  cold 
water.  Stir  the  water  with  the  thermometer  immediately 
after  adding  the  lead,  and  take  the  temperature.  Record 
this  in  the  table. 

In  case  you  have  not  determined  in  a  previous  experi- 
ment the  water  equivalent  of  your  calorimeter,  obtain  its 
value  from  the  instructor. 

OBSERVATIONS 

Weight  of  lead  cylinder g. 

Weight  of  cold  water g. 

Water  equivalent  of  calorimeter g. 

Temperature  of  the  lead °  C. 

Temperature  of  cold  water °  (7. 

Temperature  of  lead  and  water  in  calorimeter  °  C. 

Make  simple  outline  drawings,  showing  the  three  steps 
in  the  experiment,  and  describe  the  method  with  reference 
to  these  drawings. 

The  weight  of  the  cold  water  plus  the  water  equivalent 
of  the  Calorimeter,  multiplied  by  their  rise  in  temperature, 
gives  the  number  of  calories  gained  by  the  cold  water  and 


212  LABORATORY  EXERCISES 

the  calorimeter.     Record  this  value  in  a  tabular  form  near 
the  top  of  the  right-hand  page. 

This  heat  gained  by  the  water  and  the  calorimeter  was 
given  out  by  the  lead  in  cooling.  Assuming  the  lead  to 
be  at  the  temperature  of  boiling  water,  compute  the  deci- 
mal part  of  a  calorie  given  out  when  one  gram  of  lead 
cools  one  degree  Centigrade. 

CALCULATED  RESULTS 

Weight  of  water  +  water  equivalent  of  calo- 
rimeter    g. 

Temperature  change  of  water  and  calorimeter  °  G. 

Total  calories  gained  by  water  and  calorimeter  cal. 

Total  calories  given  out  by  lead  in  cooling. °  0.  cal. 

Total  calories  given  out  by  lead  in  cooling  1°  O.  cal. 

Calories  given  out  by  1  gram  of  lead  in  cooling 

1°(7. cal 

Discussion : 

Why  is  it  desirable  to  have  the  temperature  to  which  the 
water  is  raised  by  the  lead,  the  same  as  the  temperature  of 
the  room  ? 

Conclusion : 

Define  specific  heat.  What  do  you  find  the  specific 
heat  of  lead  to  be  ? 


COOLING  THROUGH  CHANGE  OP  STATE       213 
EXPERIMENT  59 

Cooling  through  Change  of  State 

OBJECT.  To  observe  the  heat  changes  taking  place  during  the 
solidification  of  acetamid.1 

APPARATUS.  Four-inch  test  tube,  three  fourths  full  of  acetamid 
crystals,  and  provided  with  a  one-hole  stopper,  through  which 
passes  a  thermometer  (0°  C.  to  100°  C.)  ;  ring  stand  with  one 
ring,  wire  gauze,  and  clamp  for  test  tube;  Bunsen burner ;  beaker 
of  water. 

Introductory : 

When  we  melt  ice  by  the  use  of  heat,  we  notice  that  it 
takes  considerable  time.  Heat  energy  must  be  entering 
the  ice,  and  yet  does  not  warm  it.  This  heat  energy 
is  used  up  in  melting  the  ice.  In  order  to  freeze  water 
back  into  ice,  this  heat  energy  must  come  out  of  the 
water.  Tubs  of  water  are  sometimes  placed  in  cellars  to 
prevent  vegetables  from  freezing.  As  the  temperature  of 
the  cellar  falls,  the  water  begins  to  freeze  first.  In  so 
doing,  it  gives  out  heat  enough  to  prevent  the  air  from 
falling  as  far  below  the  freezing  point  as  it  otherwise 
would  do.  Heat  continues  to  be  given  out  by  the  water  as 
long  as  it  is  freezing. 

It  is  possible  to  observe  these  changes  more  easily  in 
some  other  substances  than  it  is  in  ice.  When  we  melt 
substances  and  then  allow  them  to  crystallize,  they  give 
out  the  same  amount  of  heat  which  is  needed  to  melt  the 
crystals.  This  heat,  which  becomes  apparent  on  solidifi- 
cation, makes  the  substance  warm  the  containing  vessel 

luHypo"  (sodium  thiosulphate)  may  be  substituted  for  acetamid,  but 
the  results  are  not  as  satisfactory.  If  hypo  is  used,  the  tube,  after  the 
hypo  has  been  melted,  will  need  to  be  cooled  in  a  beaker  of  cold  water. 


214 


LABORATORY   EXERCISES 


and  surrounding  objects.  We  wish  to  observe  the  changes 
in  temperature  before,  during,  and  after  the  crystallization 
process  in  some  melted  acetamid. 

Experimental : 

Support  a  test  tube  containing  crystals  of  acetamid 
in  a  beaker  of  water  on  a  ring  stand  (Fig.  77).  Melt  the 
acetamid  by  heating  the  water.  As  soon  as  it  is  com- 
pletely liquefied  the  thermometer  should  be  inserted  in  the 
acetamid,  so  that  the  bulb  shall  be  entirely  covered.  If 
necessary,  continue  to  apply  heat 
until  the  temperature  is  above 
90°  C.,  but  not  over  95°  C.  In 
all  readings,  tenths  of  a  degree 
should  be  estimated. 

Remove  the  burner  and  the 
beaker  of  water,  and  allow  the 
tube  to  cool  in  air,  without  be- 
ing disturbed  in  any  way.  Every 
half  minute  take  a  reading  of  the 
temperature.  The  tube  should 
be  closely  watched  at  all  times, 
and  at  the  instant  solidification 
begins,  a  reading  should  be  taken 
and  marked  >S  in  the  table,  to 
distinguish  this  point.  Continue 
the  readings  at  half-minute  inter- 
^  vals,  until  solidification  is  com- 
plete, and  then  at  one-minute 
intervals  until  a  temperature  of 
about  55°  C.  is  reached.  At  the  close  of  the  experiment 
the  tube  and  thermometer  should  be  returned  to  the  in- 
structor, without  any  attempt  to  remove  the  thermometer 
from  the  acetamid. 


(,; 


Fig.  77. 


COOLING  THROUGH  CHANGE  OF  STATE        215 

Record  the  observations  in  tabular  form  near  the  top  of 
the  left-hand  page. 

OBSERVATIONS 

Time  in  minutes      .     0       J       1       1 J       2       2  J,  etc. 
Temperature  in  °  0.  —    —    —      —     —      — ,  etc. 

An  outline  drawing  of  the  apparatus  and  a  brief  descrip- 
tion of  the  operations  should  be  placed  immediately  below 
the  table  of  readings. 

Curve.  —  On  a  sheet  of  cross-section  paper,  plot  a  curve 
from  your  readings.  Allow  two  horizontal  spaces  (2  mm.) 
for  a  half  minute,  and  one  vertical  space  (1  mm.)  for  one 
degree.  This  curve  is  to  be  pasted  by  its  edge  to  the  top 
edge  of  the  right-hand  page. 

Discussion : 

Answer  each  question  with  a  complete  sentence. 

Is  there  any  point  where  the  temperature  curve  takes  a 
sudden  change  ?  Does  this  correspond  to  any  change  in 
the  condition  of  the  acetamid  ?  Does  your  curve  indicate 
that  acetamid  has  a  definite  melting  (or  freezing)  point  ? 
If  so,  at  what  temperature?  Is  this  temperature  main- 
tained while  solidification  is  taking  place  ?  Is  heat  required 
to  keep  a  body  at  a  temperature  above  that  of  the  room  ? 
As  no  heat  is  being  applied  externally,  from  what  change 
in  the  acetamid  must  this  heat  come  ? 

Conclusion : 

Does  a  substance  give  out  heat  or  absorb  heat  during 
solidification  ? 


216  LABORATORY  EXERCISES 

EXPERIMENT    60 

Melting  Points  and  Boiling  Points       t 

OBJECT.  To  learn  the  method  of  determining  the  melting  points 
and  boiling  points  of  substances  ;  and  to  study  the  boiling  points  of 
a  mixture  of  alcohol  and  water. 

APPARATUS.  Ring  stand  ;  ring ;  two  burette  clamps  ;  asbestos 
square,  or  iron  gauze  with  asbestos  center;  beaker  (100  cm.3)  ; 
glass  stirrer ;  thermometer ;  rubber  band  (section  of  rubber  tub- 
ing ;  capillary  tubes  ; l  distilling  flask  (60  cm.3)  ;  cork  to  fit  flask 
and  perforated  to  admit  thermometer  ;  small  Liebig  condenser,  or 
2  ft.  length  of  \"  tubing,  with  cork  stopper  perforated  to  admit 
delivery  tube  of  distilling  flask ;  glass  beads  or  a  few  short  pieces 
of  glass  tubing;  small  graduate  (preferably  25  cm.3)  ;  Bunsen 
burner. 

MATERIAL.  Stearic  acid  ;  naphthalene  or  moth-balls ;  carbon 
tetrachloride ;  grain  alcohol. 

Introductory : 

The  melting  point  of  a  substance  is  the  transition  tem- 
perature between  its  solid  and  liquid  state.  The  boiling 
point  marks  the  boundary  between  the  liquid  and  the 
gaseous  states.  A  considerable  change  in  pressure  is 
necessary  to  affect  the  melting  point  of  a  solid  ;  the 
temperature  at  which  a  liquid  boils  changes  with  even  the 
ordinary  variations  of  atmospheric  pressure. 

Determinations  of  the  melting  point  are  valuable  in 
that  they  indicate  the  purity  of  a"  substance.  A  pure  sub- 

1  The  capillary  tubes  are  made  by  heating  the  middle  of  a  short  piece 
of  glass  tubing.  When  the  tubing  is  soft  in  the  heated  portion,  draw  it 
out  into  a  thin-walled  tube  about  1  mm.  in  diameter.  With  a  file  cut  off 
lengths  of  2"  to  3"  and  seal  the  narrower  end  of  each  in  the  Bunsen 


MELTING  POINTS  AND  BOILING  POINTS       217 


stance,  melting  at  a  certain  definite  temperature,  melts 
below  that  temperature  when  it  contains  even  a  very  small 
amount  of  another  substance.     Crystal- 
line  solids   are   characterized   by  very 
definite  melting  points. 

Boiling  points  are  very  useful  in  the 
identification  of  liquids  and  as  an  indi- 
cation of  their  purity.  In  the  purifica- 
tion or  separation  of  liquids  by  distilla- 
tion, the  observed  boiling  points  are  the 
guides  to  the  steps  in  the  process. 

Experimental : 

Melting  Points.  —  («)  Light  the 
burner  underneath  the  beaker  of  water 
(Fig.  78).  Have  a  very  small  flame,  so 
that  the  water  will  heat  very  slowly. 

Put  the  open  end  of  a  capillary  tube 
into  some  stearic  acid,  so  as  to  get  a 
column  of  the  solid  several  millimeters  in  length.  Turn 
the  tube  upright  and  tap  the  closed  end  gently  on  the 
table,  so  that  most  of  the  solid  falls  to  the  bottom  of  the 
tube.  Slip  the  tube  through  the  rubber  band  (Fig.  78,  #) 
on  the  thermometer  so  that  the  solid  is  in 
the  position  indicated  in  Fig.  78. 

Move  the  glass  stirrer1  up  and  down  in 
the  beaker  until  you  see  some  of  the  small 
particles  sticking  to  the  capillary  walls  melt. 
Read  the  temperature  and  record  it  as  the 
melting  point  of  the  stearic  acid  in  a  tabular  form  on 
the  left-hand  page.  In  case  you  heated  the  water  too 


Fig.  78. 


Fig.  79. 


1  The  bottom  of  the  glass  stirrer  is  most  conveniently  made  by  bending 
the  glass  into  a  triangular  form  as  shown  in  Fig.  79. 


218  LABORATORY   EXERCISES 

rapidly,  let  it  cool  a  little  and  approach  the  melting  point 
more  cautiously,  using  a  fresh  tube  of  the  stearic  acid. 

(i)  Determine  in  a  similar  manner  the  melting  point  of 
naphthalene  (the  principal  constituent  of  moth  balls). 

(c)  Put  15  cm.3  of  carbon  tetrachloride  into  a  small 
distilling  flask  having  the  delivery  tube  pointing  upward 
as  you  pour  the  liquid  in.  Then  arrange  the  flask  as  in 
Fig.  70,  and  pass  the  delivery  tube  of  flask  through  a  cork 
fitting  into  a  condenser,  with  a  beaker  to  receive  the  dis- 
tillate. A  few  short  pieces  of  glass  tube  in  the  flask  will 
save  time  in  bringing  the  liquid  to  a  boil.  Take  as  the 
boiling  point  of  the  carbon  tetrachloride,  the  steady  tem- 
perature obtained  as  the  liquid  distills  off  through  the  de- 
livery tube.  Record. 

Remove  the  burner  and  empty  the  distilled  and  the  un- 
distilled  tetrachloride  into  the  bottle  indicated  by  the 
instructor. 

(cZ)  After  rinsing  out  the  distilling  flask  and  the  beaker 
with  a  very  little  grain  alcohol,  pour  into  the  flask  15  cm.3 
of  alcohol  and  14  cm.3  of  water.  This  gives  a  mixture 
which  is  very  nearly  50  per  cent  alcohol. 

Have  at  hand  a  sheet  of  cross-section  paper.  Accord- 
ing to  a  scale  given  by  the  instructor,  temperatures  are  to 
be  plotted  on  the  vertical  axis  and  the  volumes  (cm.3)  of 
the  distillate  on  the  horizontal  axis. 

Heat  the  diluted  alcohol  to  boiling,  and  plot  as  the  first 
temperature  that  obtained  when  the  liquid  begins  to  con- 
dense in  the  delivery  tube  of  the  flask.  Read  the  tem- 
perature from  this  point  on  as  soon  as  each  successive 
3  cm.3  of  the  distillate  is  collected.  Plot  the  readings  as 
soon  as  made.  Paste  the  cross-section  paper  by  an  edge 
in  the  note-book. 


MELTING  POINTS  AND  BOILING  POINTS       219 

OBSERVATIONS 

Melting  points,  Stearic  acid °O. 

Naphthalene '    .         °<7. 

Boiling  point,  Carbon  tetrachloride     ....         °  C. 

Make  drawings  showing  both  the  melting-point  and 
the  boiling-point  apparatus.  Describe  the  experimental 
methods  with  reference  to  these  drawings. 

Discussion : 

The  boiling  point  of  ordinary  alcohol  is  78.4°  C.  .  What 
effect  does  the  water  in  the  50  per  cent  alcohol  have  on  the 
boiling  point  of  the  alcohol  ?  Between  what  tempera- 
tures does  most  of  the  alcohol  distill  ?  (Examine  the 
curve.)  How  many  cubic  centimeters  of  distillate  were 
collected  between  these  two  temperatures  ?  What  liquid 
is  present  in  the  larger  amount  during  the  latter  part  of 
the  distillation  ?  What  makes  you  think  so  ?  Is  the  boil- 
ing point  of  water  raised  when  it  contains  a  little  alcohol  ? 

Conclusion : 

What  difference  do  you  notice  between  the  boiling 
point  of  a  pure  substance  and  the  boiling  point  of  a  solu- 
tion ?  How  does  a  liquid  dissolved  in  a  second  liquid 
affect  the  boiling  point  of  the  second  liquid  ? 


220  LABORATORY   EXERCISES 

EXPERIMENT    61 

Heat  Changes  during  Solution  and  Evaporation 

OBJECT.  To  observe  the  heat  changes  which  accompany  solu- 
tion and  evaporation. 

APPARATUS.  Centigrade  thermometer ;  50  cm.3  beaker ; 
wooden  block;  bicycle  pump  or  foot  bellows;  two  100  cm.3 
Erlenmeyer  flasks ;  battery  jar  or  other  receptacle  for  hypo  solu- 
tion ;  test  tube. 

MATERIAL.  Strips  of  cheesecloth  one  inch  wide ;  alcohol ; 
ether ;  "  hypo  "  crystals  ;  supersaturated  solution  of  hypo,  made 
by  dissolving  100  g.  of  hypo  in  20  cm.3  of  water  for  each  100  cm.3 
flask. 

Introductory : 

Photographers  notice  that  a  freshly  made  "  hypo  "  solu- 
tion feels  much  colder  than  the  water  used  in  making  it. 
Is  there  an  actual  fall  of  temperature  during  solution  ? 

Camphor  is  rubbed  on  the  head  for  headache ;  alcohol 
baths  are  given  to  fever  patients.  On  a  hot  day  we  feel 
cooler  in  a  breeze.  In  each  of  these  cases  rapid  evapora- 
tion takes  place  on  the  skin.  Is  or  is  not  the  body  actually 
cooled  by  this  evaporation  ? 

CAUTION.  No  flame  is  to  be  allowed  in  the  laboratory  during 
this  experiment,  and  at  the  close  the  windows  should  be  opened  wide. 

Experimental : 

(a)  A  thermometer  bulb  is  wrapped  with  a  strip  of 
cheesecloth,  which  is  then  tied  with  a  raveling  from  the 
cloth.  The  thermometer  is  held  by  the  upper  part  of 
the  stem  and  a  reading  taken.  Continue  to  hold  the  ther- 
mometer by  the  stem;  then  dip  the  bulb  into  a  test  tube 


HEAT  CHANGES  DURING  SOLUTION  221 

of  alcohol  and  remove  it  when  the  cloth  is  thoroughly  wet. 
The  cloth  is  allowed  to  dry,  in  a  draft  if  possible,  the 
temperature  being  constantly  watched.  Record  the  tem- 
perature (1)  immediately  before  dipping  into  the  alcohol, 
(2)  immediately  after  withdrawing  the  bulb  from  the 
alcohol,  (3)  at  the  reading  showing  the  greatest  change 
from  the  temperature  taken  in  (2).  Is  the  change  in 
temperature  that  you  noticed  due  to  the  temperature  of  the 
alcohol,  or  is  it  the  result  of  the  evaporation  of  the  alcohol? 

(6)  A  few  drops  of  water  are  placed  on  a  wooden  block 
and  a  beaker  is  set  down  in  the 'water,  so  that  there  will  be 
a  film  of  water  between  the  beaker  and  the  block.  Enough 
ether  is  poured  in  the  beaker  to  cover  the  bottom. 

Cork  the  ether  bottle  tightly  and  do  not  inhale  the  fumes  during 
the  experiment.1 

With  a  bicycle  pump  or  a  foot  bellows  having  a  piece 
of  rubber  tubing  connected  to  it,  blow  gently  on  the  sur- 
face of  the  ether  until  it  is  evaporated.  What  has  hap- 
pened to  the  water  ?  If  there  is  no  marked  change  of 
state  in  the  water,  repeat,  using  a  little  larger  amount  of 
ether.  Has  the  ether,  while  evaporating,  absorbed  heat  from 
the  water  or  lost  heat  to  it  ?  Explain. 

(<;)  Into  a  small,  clean  flask  are  placed  enough  crystals 
of  hypo  to  fill  the  flask  a  third  full.  Water,  whose  tem- 
perature has  been  observed  and  recorded,  is  added  till  the 
crystals  are  just  covered.  The  flask  is  then  shaken  vigor- 
ously with  a  rotary  motion  until  as  much  as  possible  of 
the  hypo  has  dissolved.  The  bottom  of  the  flask  is  then 
felt  with  the  hand.  Result  ?  The  thermometer  is  in- 

1  This  part  of  the  experiment  must  be  carried  on  where  there  is  a  good 
draft  to  remove  the  ether  vapor.  If  this  condition  cannot  be  met,  or  if 
the  class  is  large,  it  is  advisable  to  call  the  class  together  and  perform 
this  test  as  a  demonstration. 


222  LABORATORY  EXERCISES 

serted  in  the  solution  and  the  temperature  taken  and 
recorded.  Has  the  water  taken  heat  from  the  hypo  or  given 
heat  to  it  during  the  process  of  solution?  The  result  ob- 
tained with  hypo  is  typical  of  the  heat  change  in  solution, 
when  no  chemical  action  takes  place  between  the  dissolved 
substance  and  the  solvent. 

After  the  temperature  of  the  solution  has  been  observed, 
it  should  be  placed  in  a  receptacle  indicated  by  the  in- 
structor, so  that  the  hypo  may  be  recovered  by  the  evapo- 
ration of  the  water. 

(c?)  At  each  laboratory1  table  is  placed  one  or  more 
flasks  with  the  necks  plugged  with  cotton,  each  contain- 
ing a  supersaturated  solution  of  hypo,  which  has  stood  in 
the  room  long  enough  to  reach  room  temperature.  When 
the  students  at  a  table  have  completed  and  recorded  the 
results  of  the  preceding  parts  of  the  experiment,  they 
should  make  this  final  test  together.  Each  student  should 
touch  the  flask  with  his  finger,  without  moving  the  flask 
or  disturbing  the  liquid.  The  cotton  should  then  be 
removed  and  a  crystal  of  hypo  dropped  in.  Result? 
When  the  change  is  complete,  each  student  should  feel 
of  the  flask  and  record  his  observation.  What  heat  change 
takes  place  when  the  hypo  is  dissolved?  When  the  hypo 
comes  out  of  solution,  what  heat  change  occurs  ? 

The  results  of  Parts  (a)  and  (c)  should  be  recorded  in 
tabular  form  near  the  top  of  the  left-hand  page.  Other 
observed  results  should  be  recorded  in  the  description  of 
the  part  of  the  experiment  to  which  they  belong. 

OBSERVATIONS 
Part  (a) : 

Temperature  of  room  (1) °  Q. 

Temperature  of  alcohol  (2)     ......  °  G. 

Extreme  temperature  noticed  (3)      ....  °  0. 


HEAT  OF  FUSION  OF  ICE  223 

Part  0): 

Temperature  of  water  before  dissolving  hypo  .          °  0. 
Temperature  of  hypo  solution °  C. 

Drawings  should  be  made  of  the  apparatus  used  in 
parts  (a)  and  (6).  A  brief  description  of  the  tests  and 
of  all  results  not  noted  in  the  table  should  follow  the 
table. 

Discussion : 

Answer,  under  this  heading,  the  italicized  questions 
occurring  in  the  experimental  directions. 

Conclusion : 

Is  sensible  heat  absorbed  or  given  out  when  a  liquid 
changes  to  a  gas  ?  When  a  solid  dissolves  ? 


EXPERIMENT    62 

Heat  of  Fusion  of  Ice 

OBJECT.  To  find  the  number  of  calories  of  heat  required  to 
change  one  gram  of  ice  to  water  without  warming  the  ice  water 
above  the  melting  point  of  the  ice. 

APPARATUS.  Calorimeter ;  thermometer  ;  graduate,  or  balance 
and  weights  ;  150  cm.3  beaker. 

MATERIAL.  Supply  of  ice  cracked  into  pieces  about  the  sizo 
of  a  hickory  nut ;  supply  of  hot  water  at  about  50°  C. 

Introductory : 

When  water  at  boiling  temperature  is  thrown  upon  ice 
that  is  just  ready  to  melt,  some  ice  will  melt  and  the 
boiling  water  will  be  cooled  down  to  the  freezing  point. 
If  just  enough  boiling  water  to  melt  the  ice  is  used,  it  will 


224  LABORATORY  EXERCISES 

be  found  that  there  will  be  one  and  a  quarter  times  as 
much  ice  melted  as  there  was  boiling  water,  and  the  whole 
mass  will  be  ice  cold. 

What  becomes  of  the  heat  that  was  in  the  boiling 
water  ?  When  heat  is  continuously  applied  to  a  solid 
body,  as  when  pieces  of  ice  are  stirred  about  quickly  in  a 
pan  on  a  hot  stove,  the  solid  is  heated  only  up  to  the 
melting  temperature.  If  stirred  vigorously,  the  melted 
part  and  the  part  not  yet  melted  do  not  get  warmer  than 
the  melting  temperature  until  the  last  bit  is  melted. 
After  this  the  liquid  will  get  warmer. 

We  wish  to  find  how  much  heat  must  be  applied  and 
must  disappear  as  heat  energy,  when  we  change  a  definite 
amount  of  a  solid  to  its  liquid  state.  This  number  of 
calories  is  called  the  heat  of  fusion  of  the  substance. 

Experimental : 

(a)  In  the  calorimeter  are  to  be  placed  300  cm.8  of  hot 
water.1  Since  the  calorimeter  is  being  heated  or  cooled 
at  the  same  time  as  the  water  in  it,  this  fact  must  be  taken 
into  account  in  the  calculations.  The  number  of  grams 
of  water  which  require  the  same  amount  of  heat  to  raise 
them  one  degree  as  is  required  to  raise  the  temperature  Qf 
the  calorimeter  one  degree,  will  be  furnished  by  the  in- 
structor. This  number  of  grams,  called  the  water  equiva- 
lent of  the  calorimeter,  is  always  to  be  added  to  the 
number  of  grams  of  water  actually  placed  in  the  calo- 
rimeter. 

(6)  Insert  the  thermometer  into  the  water,  and  when 
the  temperature  becomes  about  50°  C.,  begin  to  add  dry 

1  If  the  instructor  prefers,  the  masses  of  water  and  ice  may  be  found 
by  direct  weighing.  The  method  of  measurement  used  here  is  much 
simpler,  and  the  results  are  accurate  within  the  limits  of  error  which  may 
be  expected  in  the  experiment. 


HEAT  OF  FUSION  OF  ICE  225 

ice,  and  continue  until  enough  dry  ice  to  fill  a  150  cm.8 
beaker  has  been  added.  Stir  constantly.  As  soon  as  the 
last  particle  of  ice  has  been  melted,  give  one  final  stir  and 
take  the  temperature  at  once.  Record  this  temperature 
as  well  as  the  first  temperature,  in  a  table  near  the  top  of 
the  left-hand  page. 

(<?)  Measure  the  contents  of  the  calorimeter  and  record 
the  volume  obtained. 

OBSERVATIONS 

Volume  of  hot  water cm.9 

Final  volume  of  water  and  melted  ice    .     .     .  cm.z 
Initial  temperature  (at  instant  of  beginning  to 

add  ice) °<7. 

Final  temperature  (at  melting  of  last  piece  of 

ice)        °0. 

Water  equivalent  of  the  calorimeter       ...  g. 

Calculation  of  Results.  —  (1)  Calculate,  from  the  final 
volume  of  liquid  in  the  calorimeter,  the  mass  of  ice  used. 

(2)  Calculate  the  number  of  calories  of  heat  given  up  by 
the  original  hot  water  and  the  calorimeter,  in  cooling  from 
the  initial  to  the   final  temperature.     This  is  the   total 
number  of  calories  available  to  melt  the  ice  and  warm  the 
ice    water.      Calculate  the   number   of  calories   used  in 
raising  the  temperature  of  the  melted  ice  from  0°  C.  up  to 
the  final  temperature. 

(3)  From  these  two  results  calculate: 

(a)  The  total  number  of  calories  that  were  used 

in  melting  all  the  ice. 
(6)  The  number  of   calories  needed   to  melt   one 

gram  of  ice. 

These  calculated  results  should  be  entered  in  a  table  at 
the  top  of  the  right-hand  page. 


226  LABORATORY  EXERCISES 

CALCULATED  RESULTS 

Total  hot  mass  (mass  of  water  +  water  equiva- 
lent of  calorimeter') g. 

Cold  mass  (ice)        g. 

Change  of  temperature °C. 

Calories  given  up  by  hot  water cal. 

Calories  absorbed  in  warming  melted  ice  to 

final  temperature cal. 

Calories  absorbed  in  melting  all  the  ice       .     .  cal. 

Calories  absorbed  in  melting  one  gram  of  ice  cal. 

Discussion : 

Explain  why  it  is  important  to  use  dry  ice. 
Explain  how  the  last  three  numbers  in  the  table  of  cal- 
culated results  are  obtained. 

Conclusion : 

The  heat  of  fusion  of  ice  is calories. 


EXPERIMENT    63 

Heat  of  Vaporization 

OBJECT.  To  determine  the  number  of  calories  of  heat  that  are 
liberated  when  one  gram  of  steam  at  100°  C.  is  converted  into  water 
at  100°  C. 

APPARATUS.  Boiler  ;  steam  trap  ;  glass  and  rubber  tubing  as 
shown  in  Fig.  80 ;  Bunsen  burner ;  calorimeter ;  thermometer ; 
graduate,  100  cm.3 

Introductory : 

Farmers  often  cook  a  large  quantity  of  feed  for  their 
stock  in  the  following  manner :  They  take  steam  from 


HEAT  OF  VAPORIZATION  227 

a  boiler  through  a  pipe  or  hose.  The  end  of  this  pipe  is 
pushed  down  under  cold  water  in  a  barrel.  The  cold 
water  condenses  the  steam  and  is  heated  very  quickly  by 
the  heat  which  the  steam  gives  up.  The  steam  first  gives 
up  heat  in  condensing  to  drops  of  boiling  water,  and  these 
drops  of  boiling  water  give  up  heat  while  they  cool  down 
to  the  final  temperature  of  the  wateifc  in  the  barrel.  A 
surprisingly  large  number  of  calories  of  heat  is  thus  given 
to  the  barrel  of  water,  by  a  comparatively  small  weight 
of  steam. 

Our  experiment  is  to  find  out  how  many  calories  of  heat 
are  given  out  by  one  gram  of  steam  in  condensing  to  boil- 
ing water,  and  this  number  of  calories  is  the  same  as  that 
necessary  to  vaporize  one  gram  of  boiling  water,  without 
changing  the  temperature.  This  number  of  calories  is 
called  the  heat  of  vaporization. 

Experimental : 

The  boiler  is  half  filled  with  water  and  the  burner 
lighted  under  it.  While  the  water  is  coming  to  a  boil, 
400  cm.8  of  as  cold  water  as  possible  are  measured  into 
the  calorimeter.  How  many  grams  of  water  are  there  ? 
The  water  equivalent  of  the  calorimeter,  or  the  number  of 
grams  which  must  be  added  to  the  actual  mass  of  the 
water  to  allow  for  the  heating  of  the  calorimeter,  will  be 
given  by  the  instructor,  or  calculated  under  his  direction. 

In  passing  the  steam  from  the  boiler  to  the  calorimeter, 
errors  must  be  avoided  by  taking  the  precautions  which 
follow.  The  steam  must  be  free  from  water  produced  by 
condensation.  A  hot  flame  and  the  steam  trap  included 
in  the  apparatus,  will  help  to  secure  this  result.  The 
temperature  of  the  cold  water  is  to  be  taken  immediately 
before  the  steam  is  passed  into  it. 

The  delivery  tube  should  dip  far  enough  below  the  sur- 


228  LABORATORY  EXERCISES 

face  of  the  water  in  the  calorimeter  for  the  steam  to  cause 
a  rattle  as  it  condenses.  At  all  times  the  calorimeter 
should  be  shielded  as  far  as  possible  from  heat  other  than 
that  of  the  steam  passing  into  it. 

The  water  should  be  constantly  stirred  with  the  ther- 
mometer, and  its  temperature  watched.  When  it  reaches 
about  40°  C.,  the^team  tube  should  be  taken  out,  the 


Fig.  80. 

water  stirred  thoroughly,  and  the  highest  temperature 
reached  after  stirring  should  be  recorded. 

You  know  the  number  of  grams  of  water  with  which 
you  started.  By  measuring  and  recording  the  contents 
after  the  steam  has  passed,  the  mass  of  the  steam  may  be 
calculated. 

The  observed  results  are  to  be  placed  in  a  table  near  the 
top  of  the  left-hand  page. 

OBSERVATIONS 

Volume  of  cold  water cm.3 

Final  volume  of  water   .......         cm.3 


HEAT  OF  VAPORIZATION  229 

Initial  temperature  of  cold  water  and  calo- 
rimeter    °  (7. 

Final  temperature  of  calorimeter  and  contents  °  O. 

Water  equivalent  of  calorimeter g. 

A  sectional  drawing  should  be  made  to  show  the  arrange- 
ment of  apparatus  and  a  brief  description  written,  refer- 
ring to  the  drawing.  State  the  precautions  that  were  taken 
to  secure  accurate  results. 

It  is  now  possible  to  calculate  the  number  of  calories 
absorbed  by  the  cold  water,  the  number  given  out  by  the 
condensed  steam  in  cooling,  the  number  given  out  in  con- 
densing, and  finally  the  heat  per  gram  in  condensing  (heat 
of  vaporization).  These  results  should  be  entered  in  a 
table  placed  at  the  top  of  the  right-hand  page,  the  calcu- 
lations being  worked  out  immediately  below. 

CALCULATED  RESULTS 

Total  cold  mass  (mass  of  water  +  water  equiva- 
lent of  calorimeter} g. 

Weight  of  steam  condensed g. 

Change  in  temperature  of  cold  water       ...         °  C. 

Change  in  temperature  of  hot  water  (condensed 
steam) °  C. 

Calories  absorbed  by  cold  water  in  being  warmed         cal. 

Calories  liberated  by  condensed  steam  in  cooling 
to  final  temperature cal. 

Calories  liberated  by  steam  in  condensing  to 
water cal. 

Calories  liberated  by  one  gram  of  steam  in  con- 
densing   cal. 

Discussion : 

What  objection  would  there  be  in  allowing  drops  of  hot 
water  condensed  in  the  delivery  tube  to  drop  into  the  calo- 


230  LABORATORY   EXERCISES 

rimeter?     What  is  meant  by  the  heat  of  vaporization  of  a 
substance  ? 

Conclusion: 

The  heat  of  vaporization  of  water,  according  to  my 
determination,  is  ...   „  calories. 


EXPERIMENT   64 

Dew  Point 

OBJECT.  To  find  the  dew  point  at  the  temperature  of  the  labo- 
ratory. 

APPARATUS.  Bright  calorimeter  ;  thermometer ;  two  beakers  ; 
glass  stirring  rod  ;  snow,  or  shaved  ice  ;  fine  salt. 

Introductory : 

It  has  been  found  by  experiment  that  warm  air  can 
contain  much  more  water  vapor  than  cold  air.  When  a 
body  of  warm  air  saturated  with  water  vapor  meets  a  cur- 
rent of  cold  air,  condensation  occurs.  Some  of  the  water 
vapor  appears  as  mist,  fog,  or  rain.  On  a  cool  night  after 
a  hot  summer  day,  the  ground  cools  off  quickly  and  chills 
the  warm  air  laden  with  vapor,  so  that  dew  is  deposited. 
The  temperature  to  which  the  air  must  be  cooled  in  order 
that  condensation  of  water  vapor  may  occur,  is  known  as 
the  dew  point.  This  temperature  depends  upon  the  relative 
amount  of  water  vapor  in  the  air. 

Experimental : 

Place  water  to  the  depth  of  about  an  inch  in  a  brightly 
polished  calorimeter.  In  it  stand  a  thermometer  and  a 
piece  of  glass  tubing  to  serve  as  a  stirring  rod.  Place 


DEW  POINT  231 

shaved  ice  or  snow  in  one  beaker  and  fill  the  other  beaker 
with  water. 

(a)  To  the  water  in  the  calorimeter,  slowly  add  a  little 
ice  at  a  time,  stirring  thoroughly  after  each  addition. 
Continue  until  a  thin  film  of  moisture  appears  on  the  out- 
side of  the  calorimeter.  Note  the  temperature  of  the 
water  in  the  calorimeter  immediately  on  the  appearance  of 
the  moisture.  Avoid  breathing  on  the  calorimeter.  Why  ? 

A  thick  deposit  of  moisture  indicates  that  you  have 
cooled  the  water  too  rapidly  and  passed  below  the  dew 
point.  In  such  a  case,  add  small  portions  of  water  from 
the  other  beaker  and  stir  until  the  mist  disappears. 
Then  add  ice  very  slowly  until  the  dew  point  is  reached. 

If  the  air  in  the  laboratory  is  very  dry  or  quite  cool,  it 
may  be  necessary  to  add  a  little  salt  to  the  crushed  ice 
in  order  to  reach  the  dew  point. 

(5)  Start  with  a  thin  film  of  moisture  on  the  outside  of 
the  calorimeter,  but  have  the  vessel  less  than  half  full  of 
the  cooled  water.  Stirring  all  the  time,  note  the  temper- 
ature at  which  the  moisture  disappears.  This  temperature 
should  be  within  a  degree  of  that  obtained  in  (a). 

OBSERVATIONS 

Temperature  at  which  moisture  appears .     .     .          °C. 
Temperature  at  which  moisture  disappears.     .  °(7. 

Make  a  simple  drawing  of  your  apparatus  and  describe 
the  method  briefly. 

Take  for  the  dew  point  the  average  of  the  temperatures 
at  which  the  mist  appears  and  disappears. 

Discussion : 

Just  what  air  was  cooled  to  its  dew  point  in  this  deter- 
mination ?  If  the  air  in  the  room  were  nearly  saturated 


232  *    LABORATORY   EXERCISES 

with  water  vapor,  would  the  amount  of  cooling  necessary 
to  reach  the  dew  point  be  small  or  great?  Explain. 
How  would  you  find  the  dew  point  of  the  outdoor  air  on 
a  cold  day  ? 

Conclusion : 

Define  the  dew  point.     Complete  the  following  : 

The  dew  point  of  the  air  in  the  laboratory  at on 

was °C.  (time) 

(date) 


EXPERIMENT    65 

Magnetic  Induction 

OBJECT.  To  study  the  behavior  of  iron,  steel,  and  other  materials 
in  a  magnetic  field. 

APPARATUS.  Strong  bar  magnet ;  pocket  compass ;  small 
pieces  of  iron,  copper,  tin  plate,  granulated  tin,  nickel,  pasteboard, 
glass;  pieces  of  watch  spring;  sheets,  at  least  2  inches  square, 
of  pasteboard,  glass,  copper,  iron,  tin  plate ;  blocks  or  other 
supports  for  magnet  and  compass  ;  iron  filings  or  small  brads. 

Introductory : 

The  most  familiar  property  of  a  magnet  is  its  ability  to 
attract  iron  and  steel.  But  when  two  magnets  are 
brought  near  each  other,  only  unlike  poles  attract,  while 
like  poles  repel.  A  few  simple  tests  of  the  behavior  of 
iron  and  steel  in  a  magnetic  field  will  give  the  principal 
facts  of  magnetic  induction.  By  this  term  we  mean  the 
production  of  magnetic  properties  in  iron  and  steel  by 
placing  these  materials  in  a  magnetic  field.  Other  mate- 
rials will  also  be  examined,  to  determine  whether  magnetic 
\nduction  takes  place  in  them  as  well. 


MAGNETIC  INDUCTION  233 

Experimental : 

(a)  A  magnet  is  successively  brought  near  small  pieces 
of  iron,  steel,  copper,  "  tin  "  (sheet  iron  coated  with  tin), 
granulated  tin,  nickel,  pasteboard,  glass.  Record  in  tabu- 
lar form  at  the  top  of  the  left-hand  page  under  the  head- 
ing "  Magnetic  "  the  names  of  the  materials  attracted,  and 
under  "  Non-magnetic,"  those  not  attracted. 

(6)  A  piece  of  soft  iron  is  held  near  a  magnet,  but  does 
not  touch  it.  Some  iron  filings  or  small  brads  are  then 
brought  in  contact  with  the  other  end  of  the  piece  of  iron. 
Note  and  record  the  result.  Without  jarring  the  iron, 
the  magnet  is  then  withdrawn  carefully  and  the  effect  on 
the  iron  filings  noted  and  recorded.  The  same  test  is 
made  with  a  piece  of  hard  steel  (watch  spring)  in  place 
of  the  soft  iron,  and  the  results  noted. 

(c)  The  tests  in  (6)  are  repeated  with  a  magnetic 
needle  instead  of  iron  filings,  and  the  results  noted. 

(c?)  Unmagnetized  pieces  of  iron  and  steel  are  next 
stroked  with  a  magnet  in  the  manner  directed  by  the 
instructor,  and  then  tested  with  iron  filings  as  in  (6),  and 
all  results  noted. 

(e)  The  magnet  and  the  compass  needle  are  placed  on 
convenient  supports  at  such  a  distance  apart  as  the  instruc- 
tor may  direct.  Sheets  of  pasteboard,  glass,  copper,  iron, 
"  tin "  (iron  coated  with  tin),  are  successively  brought 
between  the  magnet  and  the  needle,  and  the  effect  on  the 
angle  of  deflection  of  the  needle  noted. 

A  brief  description  of  each  of  the  tests  made  should  be 
written  on  the  left-hand  page  of  the  note-book  immediately 
after  making  the  test,  and  the  results,  except  in  Part  (a), 
should  be  written  directly  opposite  on  the  right-hand 
page.  The  following  table  should  be  filled  out  for  part 
(a). 


234  LABORATORY   EXERCISES 

OBSERVATIONS 

MAGNETIC  SUBSTANCES  NON-MAGNETIC  SUBSTANCES 


After  all  the  observations  have  been  recorded,  the  dis- 
cussion should  be  written  on  the  second  right-hand  page. 

Discussion : 

Compare  the  poles  produced  at  the  near  and  at  the  re- 
mote end  of  the  induced  magnet  with  the  inducing  pole  of 
the  permanent  magnet.  What  reason  have  you  for  believ- 
ing that  there  is  a  pole  at  the  end  of  the  iron  near  the  in- 
ducing pole  ? 

What  effect  does  decreasing  the  distance  between  the 
iron  and  the  magnet  have  on  the  strength  of  the  induced 
poles  ?  (Compare  results  in  (<2)  with  those  in  (a)  and 

<?)0 

Is  the  reading  of  a  compass  needle  affected  by  the  brass 
and  glass  case  in  which  it  is  mounted  ?  What  material 
would  you  use  to  make  a  shield  to  protect  a  watch  from 
becoming  magnetized  ? 

Conclusion : 

(a)  Explain,  on  the  basis  of  the  results  obtained  in  this 
experiment,  the  attraction  of  a  piece  of  iron  or  steel  by  a 
magnet. 

(5)    Compare  iron  and  steel  with  respect  to  — 

(1)  the  ease  with  which  they  may  be  magnetized  ; 

(2)  the  permanence  of  the  magnetization. 


MAGNETIC  LINES  OF  FORCE  235 

EXPERIMENT    66 

Magnetic  Lines  of  Force 

OBJECT.  To  find  the  direction  of  the  lines  of  force  in  certain 
magnetic  fields. 

APPARATUS.  Two  6-inch  bar-  magnets  ;  2-inch  bar  magnet 
(this  may  be  replaced  by  one  of  the  larger  magnets)  ;  horseshoe 
magnet ;  cardboard ;  tin  pepper  box  of  iron  filings,  which  have 
been  heated  to  thoroughly  dry  them  ;  two  half-meter  sticks  or  a 
board  grooved  to  hold  the  magnets. 

Introductory 

If  a  piece  of  iron  is  placed  in  the  neighborhood  of  a 
magnet,  it  is  subject  to  a  force  proceeding  from  the 
magnet.  This  magnetic  force  acts  in  definite  lines,  called 
lines  of  force.  When  a  magnetic  needle  is  brought  into 
the  field  of  a  magnet,  it  always  places  itself  tangent  to  a 
line  of  force.  Iron  filings,  when  brought  into  a  magnetic 
field  and  allowed  to  move  freely,  become  tiny  magnetic 
needles  and  so  arrange  themselves  along  lines  of  force. 
By  covering  a  magnet  with  a  piece  of  cardboard  and 
sifting  filings  lightly  over  the  cardboard,  then  tapping 
the  cardboard  gently,  we  allow  the  filings  to  move  freely 
into  position  along  the  lines  of  force  in  the  part  of  the  field 
occupied  by  the  cardboard. 

Experimental  : 

The  outlines  of  the  magnets,  as  shown  in  Figs.  81  and 
82,  should  be  drawn  in  your  book  before  you  come  to  the 
laboratory,  in  order  that  the  magnetic  field  in  each  case 
may  be  recorded  promptly. 

(a)  Lay  the  bar  magnet  on  the  table  and  place  the  card- 
board over  it,  using  the  half-meter  sticks  as  supports. 


LABORATORY   EXERCISES 


IZ 


Sprinkle  iron  filings  lightly  on  the  cardboard  with  the 
sifter  held  at  some  distance  above  the  table.  Tap  the 
cardboard  gently  to  permit  the 
filings  to  arrange  themselves. 
When  a  distinct  representation 
of  the  magnetic  field  is  obtained, 
make  an  outline  drawing  of  it 
in  the  upper  half  of  the  right- 
hand  page  of  your  note-book. 
Be  sure  that  your  drawing 
shows  the  location  of  the  definite 
lines  of  force  along  which  the 
iron  filings  arrange  themselves. 
Draw  a  few  lines  only  to  show 
the  general  shape  of  the  field, 


r~N\ 


Fig.  81.     First  Right-hand 
Page. 


and  do  not  try  to  represent  all  the  filings. 

(5)  Slide  the  filings  from  the  cardboard  on  to  a  sheet  of 
paper  and  return  them  to  the  shaker.  Arrange  the  two  bar 
magnets  with  their  unlike  poles 
facing  each  other  and  about  3 
cm.  apart.  Secure  a  map  of 
the  magnetic  field  on  cardboard 
with  iron  filings  as  before,  and 
sketch  in  the  lower  left  corner 
of  the  right-hand  page. 

(<?)  In  a  similar  manner,  map 
the  field  between  two  like  poles 
and  record  in  the  other  corner  of 
the  right-hand  page. 

(c?)  Place  the  small  magnet 
at  right  angles  to  one  end  of  one 
of  the  large  magnets  and  about 
3  cm.  distant.     Map  the  field  as  before,  and  make,  a  draw- 
ing of  it  in  the  upper  half  of  the  next  left-hand  page. 


Fig.  82.     Second  Left-hand 
Page. 


MAGNETIC  LINES  OF  FORCE  237 

(«)  Map  the  field  in  the  vicinity  of  the  poles  of  a  horse- 
shoe magnet,  representing  it  in  the  lower  half  of  the  second 
left-hand  page. 

Write  a  brief  description  of  the  method  employed  to 
map  the  fields.  No  other  drawing  is  necessary. 

Conclusion : 

Do  opposite  poles  seem  to  be  drawn  together  or  pushed 
apart  ?  What  is  the  effect  with  like  poles  ?  What  special 
advantage  is  there  in  the  horseshoe-shaped  magnet  ? 


238  LABORATORY   EXERCISES 

EXPERIMENT    67 

Development  of  an  Electrostatic  Series 

OBJECT.  To  arrange  various  substances  in  such  an  order  that 
each  will  be  positively  electrified  when  rubbed  with  the  substance 
following  it  in  the  series  and  negatively  electrified  by  the  preceding 
substance. 

APPARATUS.  Gold-leaf  electroscope ; l  four  blocks  of  wood 
with  hard  rubber  handles,  having  the  following  substances  ce- 
mented to  them :  a  sheet  of  glass,  a  sheet  of  hard  rubber,  a 
piece  of  silk,  a  piece  of  cat's  fur. 

CAUTION.  All  the  above  substances  must  be  thoroughly  dry  and, 
if  possible,  warm  when  they  are  used.  They  should  be  carefully 
tested  before  the  laboratory  period,  to  determine  that  they  are  in  a 
non-conducting  condition.  If  atmospheric  conditions  are  bad,  the 
experiment  should  not  be  attempted. 

Introductory : 

The  attraction  of  light  objects  by  rubbed  amber  was 
the  first  electrical  experiment  ever  made.  The  behavior 
of  electric  charges  was  investigated  quite  thoroughly 
before  current  electricity  was  produced,  and  modern 

1  A  convenient  electroscope  is  shown  in  Fig.  83.  An  8-oz.  wide- 
mouth  bottle  has  a  strip  of  tin  foil  fastened  with  shellac  across  the  bottom 
outside,  up  one  side,  and  through  the  neck  of  the  bottle  down  the  same 
side  within,  across  the  bottom  and  up  the  other  inside  face  of  the  bottle 
to  the  bottom  of  the  neck.  In  this  way  the  electroscope  can  be  thor- 
oughly grounded  and  danger  of  overcharging  avoided.  The  rod  of  the 
electroscope  is  of  }"  brass,  bent  into  a  flat  square  at  the  top,  as  shown  in 
Fig.  84  and  filed  to  a  double  bevel  at  the  bottom.  This  rod  is  passed  through 
the  opening  of  a  one-hole  rubber  stopper  to  such  a  distance  that  it  will 
reach  to  about  the  middle  of  the  bottle,  and  the  hole  is  then  filled  with 
melted  sulphur,  to  better  insulate  the  rod.  A  gold  leaf,  about  an  inch 
long,  is  then  attached  with  shellac  to  each  of  the  beveled  surfaces.  The 
stopper,  with  the  rod  and  leaves,  is  then  inserted  in  the  neck  of  the  bottle, 
care  being  taken  not  to  break  the  tinfoil  on  the  side  of  the  neck. 


DEVELOPMENT  OF  AN   ELECTROSTATIC  SERIES      239 


theories  of  electricity  have  a  great  deal  to  say  about 
electric  charges.  As  a  matter  of  agreement  among  scien- 
tists, the  charge  produced  on  glass, 
when  rubbed  with  silk,  is  called  positive 
(  +  );  that  produced  on  sealing  wax, 
when  rubbed  with  flannel,  is  negative 
(  — ).  These  are  only  relative  terms. 
In  our  experiment  we  shall  seek  to 
establish  a  graduated  series,  with  the 
most  positive  at  the  top  and  the  most 
negative  at  the  bottom. 


Experimental : 

The  electroscope  is  charged  positively 
by  induction,  using  the  hard  rubber 
plate  rubbed  with  the  cat's  fur.  The 
hard  rubber  plate  after  it  is  negatively 
charged  by  the  cat's  fur,  is  again  brought 
down  carefully  from  above  to  within  a 
centimeter  of  the  top  of  the  electro- 
scope and  its  effect  on  the  divergence 
of  the  leaves  noted.  A  similar  test  is 
made  with  the  positively  charged  fur.  The  effect  of  each 
of  these  charged  bodies  on  the  divergence  of  the  leaves 
should  be  recorded,  as  these  results  are  the  standard  with 
which  we  shall  compare  the  results  obtained 
with  the  other  pairs  of  substances  tested. 
In  the  table  record  fur  as  4-  and  hard  rubber 


Fig.  83. 


The  charge  on  the  hard  rubber  plate  is 
then  removed  by  holding  the  finger  at  one 
edge  and  breathing  across  the  surface,  or 
by  passing  the  plate  quickly  through  a  flame.     If  there 
is  no  effect,  or  only  a  very  slight  one,  when  the  plate  is 


240  LABORATORY   EXERCISES 

again  brought  near  the  electroscope,  the  plate  may  be  con- 
sidered as  discharged.  Each  plate  must  be  similarly  dis- 
charged, before  being  rubbed  with  a  new  substance.  The 
flame  should  not  be  used  with  the  fur. 

After  both  the  glass  and  the  hard  rubber  have  shown 
by  test  that  they  have  no  charge,  they  are  to  be  rubbed 
together  and  each  in  turn  brought  down  carefully  from 
above  near  the  top  of  the  electroscope.  From  the  results 
obtained,  record  this  pair  in  the  table,  giving  each  charge 
the  proper  sign. 

Continue  to  discharge  two  substances,  then  rub  them 
together,  and  finally  determine  the  sign  of  the  charge  on 
each,  until  each  of  the  four  substances  has  been  rubbed 
with  each  of  the  others.  Record  all  results  in  the  tabular 
form,  near  the  top  of  the  left-hand  page. 

OBSERVATIONS 
Charge  Pairs  of  substances  tested : 

+  Cat's  fur        etc. 

Hard  rubber etc. 

A  careful  description  of  the  method  of  charging  the 
electroscope  and  of  the  effect  on  the  charged  electroscope 
of  the  fur  and  hard  rubber  should  be  given,  accompanied 
by  a  simple  sectional  drawing  of  the  electroscope  and  one 
of  the  plates  under  test,  with  the  charge  on  the'  plate  and 
on  the  electroscope  marked. 

Place  on  the  right-hand  page  the  following  tabular  form. 

SUMMARY  OF  RESULTS 

SUBSTANCE  NUMBER  OF  TIMES  POSITIVE  NUMBER  OF  TIMES  NEGATIVE 


THE  SIMPLE  CELL  241 

Conclusion : 

From  the  summary  of  results,  arrange  the  substances 
in  a  vertical  series,  with  the  one  positive  the  greatest 
number  of  times  at  the  top,  the  next  most  positive  next, 
and  so  on.  If  you  find  that  your  series,  as  thus  arranged, 
fulfills  the  conditions  stated  in  the  Object,  place  a  -f  sign 
above  and  a  —  sign  below  the 'column  and  make  a  state- 
ment to  the  effect  that  this  is  the  correct  arrangement  of 
the  series. 

EXPERIMENT    68 

The  Simple  Cell 

OBJECT.  To  study  the  chemical  and  electrical  action  in  a  simple 
voltaic  cell. 

APPARATUS.  Tumbler  of  sulphuric  acid  (1  :  20)  ;  strips  of  amal- 
gamated and  unamalgamated  zinc  ;  strip  of  copper  ;  galvanometer 
or  low-reading  voltmeter;1  battery  stand  or  clamps  for  holding 
elements  in  place  ;  No.  18  insulated  copper  wire  for  connections. 

Introductory : 

When  two  conductors  are  placed  in  a  solution  which 
acts  on  one  of  them  more  than  on  the  other,  a  difference 

1  It  is  the  belief  of  the  authors  that  voltmeters  and  ammeters  are  to  be 
preferred  to  galvanometers,  as  they  introduce  the  student  directly  to 
practical  units.  High-grade  commercial  instruments  of  the  d'Arsonval 
type  may  now  be  had  at  prices  which  make  the  original  investment  but 
little  more  than  that  for  galvanometers,  while  the  trouble  and  expense  of 
keeping  galvanometer*  in  order  is  far  more  than  for  the  commercial  in- 
struments. Ammeters  should  have  external  shunts ;  the  instrument 
movement  without  the  shunt  may  then  be  used  as  a  galvanometer  in 
Wheatstone  bridge  and  induction  experiments.  The  scales  recommended 
for  the  ammeters  are  12  amperes  and  1.2  amperes.  The  voltmeters  should 
have  120  volt  and  6  volt  scales.  Where  voltmeters  are  not  available, 
d'Arsonval  galvanometers  may  be  used  in  many  experiments.  Tangent 
galvanometers,  or  shunted  d'Arsonval  instruments,  may  be  substituted 
for  ammeters. 


242 


LABORATORY  EXERCISES 


of  potential  is  produced  between  the  two  conductors. 
When  they  are  joined  by  a  wire,  an  electric  current  flows 
from  one  to  the  other.  A  strip  of  zinc  and  a  strip  of 
copper  immersed  in  dilute  sulphuric  acid  constitute  a 
simple  cell.  We  wish  to  investigate  the  chemical  and 
electrical  action  that  takes  place  in  such  a  cell. 

Experimental : 

A  strip  of  zinc  and  one  of  copper,  a  tumbler  con- 
taining dilute  sulphuric  acid,  clamps  for  holding  the 
strips  in  place,  connecting  wires,  and  a  voltmeter  will  be 
furnished  you.  The  chemical  action  on  the  strips  is 
tested  by  placing  each  in  the  acid  separately,  then  both 
together,  first  unconnected  and  then  connected  (Observa- 
tions 1-4).  The  relative  number  of  bubbles  produced  at 
each  plate  should  be  noted  and  recorded  in  Observations 
1-5. 

The  order  of  operations  is  indicated  in  the  table  of 
observations,  to  which  the  numbers  in  the  text  refer. 
Where  there  is  not  room  to  write  the 
observed  result  on  the  left-hand  page, 
it  may  be  continued  on  the  same  line 
of  the  right-hand  page. 

Amalgamated  zinc  (zinc  coated  with 
mercury)  is  next  substituted  for  the 
plain  zinc  and  connected  by  a  wire  with 
the  copper  (Observation  5).  A  wire 
from  each  plate  is  separately  touched  to 
the  tongue  (Observation  6),  and  then 
both  wires  are  touched  to  the  tongue 
at  different  points  (Observation  7). 

The  wires  are  connected  to  a  voltmeter.  When  the 
needle  swings  over  the  scale  in  a  positive  direction,  the 
current  leaves  the  cell  by  the  wire  connected  to  the  plus 


Fig.  85. 


THE  SIMPLE  CELL  243 

terminal  of  the  voltmeter.  The  terminal  of  the  cell  to 
which  this  wire  is  connected  is  the  plus  electrode,  or 
cathode.  Read  the  deflection  if  the  needle  is  on  the  scale. 
Reverse  the  connections  at  the  voltmeter  and  determine 
whether  the  current  has  a  definite«direction  (Observations 
8,  9,  10). 

OBSERVATIONS  RESULTS 


1.  Copper  in  acid     . 

2.  Zinc  in  acid    .... 

3.  Both  in  acid,  unconnected 

4.  Both  in  acid,  connected 

5.  Zinc  amalgamated,  con- 

nected to  copper     . 

6.  Each    wire    touched    to 

tongue  separately  . 

7.  Both     wires   touched   to 

tongue 

8.  Copper  connected  to  volt- 

meter +  ,  reading 

9.  Zinc   connected   to   volt- 

meter +  ,  reading  . 
10.    Cathode^  +  )  plate  of  cell 
is 


Make  a  drawing  of  the  stand,  the  tumbler,  and  the 
plates,  in  the  usual  place  on  the  left-hand  page,  and  in- 
clude in  your  description  any  points  not  noted  in  the 
table. 

Explanation  of  the  Chemical  Action.  —  (Not  to  be 
written  in  the  note-book.)  The  production  of  gas  in  the 
liquid  shows  that  chemical  action  is  going  on.  The  gas 
is  hydrogen,  and  results  from  the  decomposition  of  the 
acid.  The  remainder  of  the  acid  unites  with  the  zinc, 


244  LABORATORY   EXERCISES 

forming  a  soluble  compound.  The  action  of  the  acid  on 
the  zinc,  when  the  plates  are  not  connected,  is  called 
local  action.  The  deflection  of  the  voltmeter  corresponds 
to  the  electric  pressure.  A  loss  of  electric  pressure 
after  the  cell  has  been*  in  action  for  some  time  is  due  to 
polarization. 

Discussion : 

How  is  local  action  prevented  or  diminished  ?  Why  is 
it  desirable  to  prevent  it  ?  Give  two  ways  of  showing 
the  passage  of  a  small  current  through  a  wire.  Which 
test  might  furnish  a  method  of  determining  the  direction 
of  the  current  flow  ?  How  ? 

Conclusion ; 

State  the  essential  parts  of  a  simple  cell. 


EXPERIMENT    69 

The  Two-fluid  Cell 

OBJECT.  To  study  the  prevention  of  polarization  in  the  Dan- 
iell  cell. 

APPARATUS.  Tumbler ;  porous  cup ;  battery  stand  ;  amalga- 
mated zinc ;  copper  strip ;  voltmeter  or  high  resistance  galva- 
nometer ;  resistance  box,  or  coil  of  wire  having  a  resistance  of 
about  20  ohms  ;  $  18  insulated  copper  wire. 

MATERIAL.  Dilute  sulphuric  acid  (1  :20)  ;  saturated  solution 
of  copper  sulphate. 

Introductory : 

When  the  push  button  of  a  doorbell  is  pressed  for  a  long 
time,  the  bell  will  often  stop  ringing.  A  change  has  taken 
place  in  the  battery  which  prevents  a  current  sufficient 


THE  TWO-FLUID  CELL  245 

to  ring  the  bell  from  passing.  This  change  is  an  increase 
in  resistance  and  a  decrease  in  the  difference  in  potential 
between  the  plates  of  the  cell ;  it  is  called  polarization. 
We  are  going  to  observe  the  polarization  of  a  simple  cell, 
and  see  how  it  is  prevented  in  a  two-fluid  cell,  called  the 
Daniell  cell. 

Experimental : 

(a)  A  simple  cell  is  set  up  as  in  Experiment  68.     The 
difference  of  potential  of  the  freshly  prepared  cell  is  read 
by  means  of  a  voltmeter.     The  cell  is  then  allowed   to 
send  a  current  through  a  coil  of  wire  connected   to  its 
terminals,  and  the  voltage  is  read  immediately  after  con- 
necting the  coil.     The  difference  between  this  and  the 
first  reading  is  due  to  the  fact  that  only  the  part  of  the 
pressure  which  is  driving  the  current  through  the  coil  is 
now  being  measured.     The  voltmeter  is  carefully  watched 
until   the  needle  becomes  stationary, 

when  a  reading  is  taken.  Any  differ- 
ence between  the  second  and  third 
reading  is  due  to  polarization. 

Notice  whether  there  are  hydrogen 
bubbles  on  the  copper  plate.  Record 
result.  If  bubbles  are  noticed,  rub 
them  off  with  the  finger,  and  again 
observe  the  voltmeter  reading. 

(b)  Part  of  the  acid  is  poured  into 
a  small  porous  cup.     This  is  set  into 
the  tumbler  containing  the  remainder 

of  the  acid.  The  plates  are  then  inserted,  the  zinc  into  the 
acid  in  the  porous  cup  and  the  copper  into  the  acid  in  the 
tumbler.  The  voltage  is  read  before  connecting  the  coil, 
immediately  after  connecting  the  coil,  and  when  the 
needle  becomes  stationary,  as  in  (a).  Does  the  porous  cup 


246  LABORATORY   EXERCISES 

prevent  polarization?  Notice  whether  bubbles  form,  as  in 
(a). 

(c)  Keeping  sulphuric  acid  in  the  porous  cup  around 
the  zinc,  replace  the  acid  in  the  tumbler  with  copper  sul- 
phate solution.  The  cell  now  has  zinc  in  sulphuric  acid 
and  copper  in  copper  sulphate,  and  is  known  as  a  Daniell 
cell  (Fig.  86).  Make  three  readings  of  voltage,  under  the 
same  conditions  as  in  the  preceding  parts  of  the  experi- 
ment. Does  the  copper  sulphate  prevent  polarization  ? 

Record  the  results  of  your  observations  in  tabular  form 
near  the  top  of  the  left-hand  page. 

OBSERVATIONS 

PABT  (rt)  PART  (6)  PART  (c) 

Bubbles  appear  at     .  

Voltage  before  closing  circuit 
Voltage,  circuit  just  closed 
Voltage,  needle  stationary. 

A  diagrammatic  sketch,  similar  to  Fig.  86,  should  be 
made  for  each  of  the  three  tests.  In  each  sketch,  label  each 
plate  and  the  contents  of  the  tumbler  and  the  porous  cup. 
A  very  brief  description  should  accompany  these  drawings. 

Discussion : 

How  does  the  collection  of  hydrogen  on  the  copper 
plate  affect  the  voltage  of  the  cell  ?  Which  is  more  prac- 
tical, the  simple  cell  or  the  Daniell  cell  ?  Why  ? 

Answer  also  the  questions  in  italics  occurring  in  the  ex- 
perimental directions. 

Conclusion: 

What  prevents  polarization  in  the  Daniell  cell  ? 


ELECTROPLATING  247 

EXPERIMENT    70 

Electroplating 
OBJECT.    To  electroplate  (a)  with  copper ;  (6)  with  nickel. 

APPARATUS.  Porcelain  battery  top,  or  Skidmore  battery 
stand  ;  electric  light  carbon  ;  copper  sheet  4"  x  2",  with  wire  at- 
tached ;  strip  of  pure  nickel  about  3"x  1" ;  two  storage  cells,  or 
three  Daniell  cells  ;  two  tumblers  ;  wire  for  connections  ;  reversing 
switch  (Fig.  88)  is  desirable. 

MATERIAL.  Saturated  solution  of  copper  sulphate ;  plating 
bath  of  nickel  ammonium  sulphate  ; l  rouge  cloth  or  other  polishing 
material. 

Introductory ; 

The  simplest  and  most  convenient  method  of  plating  an 
object  is  by  means  of  the  electric  current.  The  positively 
charged  metallic  ions  travel  with  the  current  and  deposit 
at  one  electrode.  The  object  to  be  plated  should  be  an 
electrode  in  a  solution  of  some  compound  of  the  metal  to 
be  deposited.  If  a  current  of  suitable  strength  is  then 
passed,  a  film  of  the  metal  coats  the  object.  To  supply 
the  place  in  the  solution  of  the  metallic  ions  deposited,  a 
strip  or  bar  of  the  plating  metal  is  hung  in  the  solution 
and  serves  as  the  other  electrode.  If  the  object  to  be 
plated  is  an  insulator,  it  must  first  be  coated  with  some 
conducting  material,  such  as  graphite.  An  object  to  be 
nickel  plated  is  usually  copper  plated  first ;  the  nickel  is 
then  plated  on  the  copper  coating. 

1  This  solution  is  made  by  dissolving  in  one  liter  of  water,  72  g.  of 
nickel  ammonium  sulphate,  23  g.  of  ammonium  sulphate,  and  5  g.  of 
crystallized  citric  acid.  Then  ammonium  hydroxide  is  added  until  the 
solution  is  no  more  than  slightly  acid  to  blue  litmus.  If,  after  some  time, 
the  solution  does  not  plate  well,  more  ammonium  sulphate  should  be 
added.  The  bath  should  always  have  a  slightly  acid  reaction. 


248 


LABORATORY   EXERCISES 


Experimental : 

(#)  Copper  Plating.  —  Fasten  an  electric  light  carbon 
in  one  clamp,  and  the  wire  attached  to  a  copper  strip  in 

the  other  clamp  of  the  stand 
or  battery  top  furnished  you. 
The  copper  should  be  bent 
into  cylindrical  form,  en- 
circling the  carbon,  but  not 
touching  it  at  any  point 
(Fig.  87).  Immerse  the 
carbon  and  the  copper  in 
a  tumbler  of  copper  sul- 
phate solution.  Is  there 
any  action  ? 

Connect  the  copper  termi- 
nal with  the  positive  termi- 
nal of  two  storage  cells  (or 
three  Daniell  cells),  connected  in  series.  Allow  the  cur- 
rent to  pass  for  five  minutes.  Withdraw  both  the  carbon 
and  the  copper  and  examine  them. 

Replace  them  in  the  solution,  reverse  the  direction  of 
the  current  through  the  plating  cell,  and  leave  them  for 
five  minutes.  Again  examine. 
Decide  upon  the  correct 
connection  for  plating  the 
carbon  and  allow  the  cur- 
rent to  pass  long  enough  to 
form  a  firm  deposit.  When 
the  carbon  is  well  coated, 
take  it  out  of  the  solution 


Fig.  87. 


Fig. 


Of  Current 

Reversing  Switch. 


and  allow  it  to  dry;    then  polish  it  with  rouge  cloth. 

Which  arrangement  of  the  carbon  and  copper  is  correct  ? 

Why  f     Upon  which  terminal,  anode  or  cathode,  is  the  metal 


ELECTROPLATING  249 

deposited?  Where  did  the  deposited  metal  come  from? 
What  is  the  use  of  the  copper  strip  ? 

(6)  Nickel  Plating.  —  Wash  all  the  copper  sulphate 
solution  from  the  clamps  for  holding  the  electrodes. 
Fasten  the  copper-plated  carbon  and  a  strip  of  nickel  in 
the  two  clamps.  Immerse  the  electrodes  in  a  tumbler  of 
nickel  ammonium  sulphate  solution.  Pass  the  current, 
making  the  nickel  the  anode,  for  five  minutes,  noting  the 
action.  The  pressure  should  be  about  2.2  volts.  When 
a  good  coating  of  nickel  is  obtained,  remove  the  cathode 
from  the  solution  and  examine  it.  Compare  the  thickness 
of  the  coating  on  the  side  near  the  nickel  electrode  with 
the  coating  on  the  other  side.  When  dry,  polish  with 
rouge  cloth. 

Would  it  be  better  if  the  nickel  anode  surrounded  the  car- 
bon, as  the  copper  anode  did? 

Make  a  simple  diagram,  showing  the  parts  of  the  plating 
cell,  and  the  direction  of  the  current  when  plating  occurs. 
Also  indicate  the  source  of  current.  With  reference  to 
the  diagram,  describe  the  operations  in  (a)  and  (6),  giving 
the  results  in  each  case. 

Discussion : 

Under  this  heading  on  the  right-hand  page,  answer  the 
questions  occurring  in  the  experimental  directions. 

Conclusion : 

Complete  the  following  statement : 

In  electroplating,  the  object  to  be  plated  is  the ,  the 

plating  metal  is  the ,  the  solution  furnishes . 


250  LABORATORY   EXERCISES 

EXPERIMENT    71 

Electrotyping 
OBJECT.    To  make  a  small  electrotype. 

APPARATUS.  Skidmore  stand  or  porcelain  battery  top  ;  copper 
strip  I"x5";  lead  strip  1"  x  5" ;  tumbler;  beaker;  three  Dan- 
iell  cells  ;  *  wire  for  connections  ;  small  brush  ;  Bunsen  burner  ; 
pieces  of  type  or  seals. 

MATERIAL.  Powdered  graphite  ;  beeswax  ;  saturated  solution 
of  copper  sulphate  ;  5  per  cent  solution  of  zinc  sulphate  ;  pieces  of 
cloth. 

Introductory : 

A  printer  in  his  smaller  job  work  prints  the  copies  from 
the  type  set  up  by  the  compositor.  When  the  number 
of  copies  desired  runs  up  into  the  thousands,  as  in  a  large 
edition  of  a  book,  the  type  metal  is  not  hard  and  durable 
enough  to  give  such  a  large  number  of  clean-cut  impres- 
sions. Accordingly  a  wax  impression  is  made  of  the  type 
as  set.  The  wax  impression,  covered  with  a  conducting 
material,  as  graphite,  is  then  electroplated  with  copper. 
The  thin  coating  of  copper,  which  has  taken  the  form  of 
the  wax  mold,  is  stripped  from  the  wax,  backed  with 
some  easily  fusible  metal,  and  mounted  on  a  wooden 
block.  In  this  way  an  electrotype  is  made  with  a  hard 
surface  of  copper  in  the  form  of  the  original  type. 

Experimental : 

Hold  the  strip  horizontally  above  a  small  Bunsen  flame, 
so  that  some  pieces  of  beeswax,  placed  on  the  upper  sur- 

1  As  the  Daniell  cells  are  run  over  night,  the  zinc  plates  should  be  well 
amalgamated  and  a  5  per  cent  solution  of  zinc  sulphate  be  used  instead 
of  sulphuric  acid.  When  not  in  use,  short-circuit  these  cells. 


ELECTROTYPING 


251 


face  of  the  strip,  will  melt  and  cover  uniformly  two  thirds 
of  the  strip  with  a  coating  about  |  inch  thick  (Fig.  89). 

When  the  wax  has  cooled  and  hardened,  rub  with  a 
cloth  finely  powdered  graphite  over  the  wax  and  beyond 
it  to  the  surface  of  the  lead,  in  order  to  prepare  a  conduct- 
ing surface.  Enough  graphite  should  be  used  to  make  a 
firm,  shiny  coating. 

Take  the  type  or  other  object  to  be  copied  and  rub 
graphite  over  its  surface.  Then 
press  the  type  into  the  wax, 
until  a  clean-cut  impression 
extends  nearly  but  not  quite 
through  the  wax,  when  the  type 
is  removed.  Dust  the  impres- 
sion again  with  graphite,  tak- 
ing care  not  to  mar  the  outline. 

With  a  brush  and  melted 
beeswax,  coat  the  back  and 
edges  of  the  lead  strip  up  to  the 
point  where  it  is  to  be  clamped. 

Clamp  the  lead  and  copper 
strips  in  place,  so  that  the 
impression  is  toward  the  copper  strip.  Immerse  the 
strips  in  a  tumbler  of  copper  sulphate  solution.  The 
electrodes  should  be  about  one  centimeter  apart.  Ar- 
range three  Daniell  cells  in  series  and  connect  them  with 
the  electrodes  in  the  plating  solution,  making  the  copper 
the  anode.  After  the  current  has  been  running  for  five 
minutes,  remove  and  examine  the  lead  strip.  Coat  with 
melted  wax  any  place  where  copper  has  been  deposited 
outside  of  the  impression  which  you  wish  to  copy. 

Return  the  electrode  to  the  solution  and  allow  the  cur- 
rent to  pass  until  the  laboratory  period  next  day. 

At  the  next  laboratory  period,  remove  and  wash  off  the 


Fig.  89. 


252  LABORATORY   EXERCISES 

lead  strip.  Immerse  it  in  hot  water  so  as  to  soften  the 
wax,  and  then  with  the  aid  of  a  knife  strip  off  the  depos- 
ited copper  carefully  in  one  piece.  The  last  pieces  of 
adhering  wax  may  be  removed  by  heating  the  copper  and 
wiping  it  with  a  cloth. 

Back  the  copper  with  melted  tin  to  the  thickness  of  | 
of  an  inch,  in  case  the  instructor  gives  directions  for  so 
doing.  Otherwise  put  the  electrotype  in  an  envelope  and 
attach  the  envelope  to  the  note-book  page  by  the  flap. 

Make  a  diagram  showing  the  arrangement  of  the  appa- 
ratus and  a  drawing  showing  the  lead  strip  with  its  coat- 
ing and  impression.  Describe  the  experimental  method 
with  references  to  these  drawings. 

Discussion : 

What  was  the  use  of  the  copper  strip  ?  Of  the  lead 
strip  ?  Why  was  the  current  allowed  to  run  all  night  ? 


EXPERIMENT    72 

The  Storage  Cell 

OBJECT.  To  study  the  construction  and  action  of  a  simple  stor- 
age cell. 

APPARATUS.  Tumbler;  two  lead  plates,  about  3"  x  1"  ;  Skid- 
more  or  other  battery  clamp  ;  voltmeter  or  galvanometer ;  elec- 
tric bell ;  ^  1 8  insulated  copper  wire  for  connections. 

MATERIAL.  Sulphuric  acid  (1  of  acid  to  8  of  water)  ;  sand- 
paper. 

Introductory  : 

The  essential  conditions  for  the  production  of  a  voltaic 
cell  are  two  different  plates  and  a  solution  that  will  react 


THE  STORAGE  CELL  253 

chemically  with  one  of  them  more  than  with  the  other. 
The  limit  to  the  usefulness  of  such  a  cell  is  reached  when 
one  of  the  plates  or  the  electrolyte  is  used  up.  This 
fact  makes  the  primary  cell  a  very  expensive  source 
of  current.  In  the  lead  secondary  or  storage  cell,  this 
difficulty  is  avoided.  The  two  plates  of  this  cell  are  alike 
before  "  charging."  The  cell  is  charged  by  passing  a  cur- 
rent through  the  plates  and  the  electrolyte.  The  latter  is 
decomposed  and  the  products  of  decomposition  add  oxygen 
to  one  plate  and  take  oxygen  from  the  other,  thus  making 
the  plates  different  chemically.  When  the  cell  is  used  as 
a  source  of  current,  a  reverse  action  takes  place  —  the 
plates  again  becoming  alike  and  the  electrolyte  being 
restored  to  its  original  form.  This  process  can  be  re- 
peated a  great  many  times  before  it  is  necessary  to  put 
in  new  plates. 

Experimental : 

(a)  The  lead  plates  are  to  be  thoroughly  cleaned  with 
sandpaper   until   the  surface   is   bright.      Then   set   the 
plates  in  a  tumbler  of  dilute  sulphuric  acid  and  clamp 
them  so  they  will  not  make  electrical 
contact    with  each    other.     Connect 
the  plates  to  a  voltmeter  or  galva- 
nometer.    Is  there  any  difference  of    —  o <— 

potential  between  the  lead  plates  when 
immersed  in  sulphuric  acid? 

(6)  Without  disconnecting  the 
voltmeter,  connect  the  two  plates  with  Fig  ^  CeU  charging. 
a  source  of  current  having  a  pressure 
of  about  4  volts.  Reverse  the  connections  of  the  meter,  if 
necessary,  so  that  the  needle  remains  on  the  scale.  Note 
the  reading  of  the  meter  ajid  record.  Observe  also 
whether  bubbles  collect  at  either  or  both  plates.  If  at 


254 


LABORATORY   EXERCISES 


both  plates,  at  which  are  they  produced  more  freely,  anode 
or  cathode  ?  Pass  the  current  for  two  minutes,  then  dis- 
connect the  source  of  current.  Observe  and. record  any 
deflection  of  the  meter  when  the  current  is  no  longer  pass- 
ing into  the  cell  from  an  outside  source.  Short-circuit  the 
cell,  by  connecting  the  plates  with  a  wire,  for  a  minute  or 
so.  Disconnect  the  short-circuiting  wire  and  again  read 
the  meter. 

(c)  Again  charge  the  cell,  this  time  for  from  5  to  10 
minutes.  At  the  end  of  the  charge  take  the  meter  reading, 
as  before.  Is  the  plate  which  is  the  anode  when  charging, 
the  anode  or  cathode  when  discharging? 

Remove  the  plates  and  observe  any  change  in  appear- 
ance that  has  taken  place.  Replace  the  plates  and  con- 
nect them  to  an  electric  bell.  Result  ?  By  short-circuit- 
ing the  cell,  bring  it  back  to  an  uncharged  condition,  as 
shown  by  the  meter. 

Most  of  the  observations  made  can  be  recorded  by  fill- 
ing in  the  proper  spaces  in  the  following  tabular  form  to 
be  placed  near  the  top  of  the  left-hand  page. 


OBSERVATIONS 


BEFORE 
CHARGING 

WHILE 
CHARGING 

FTTLLT 
CHARGED 

DISCHARGED 

Voltmeter  reading.  .  . 

Bubbles  at  anode  .  .  . 

Bubbles  at  cathode  .  . 

Color  of  anode  .... 

Color  of  cathode   .  .  . 









NOTE.   In  the  table  fill  in  spaces  marked  ( ),  but  leave  blank 

spaces  marked  ( ). 


LAWS  OF  RESISTANCE  255 

Make  a  diagrammatic  sketch  showing  the  connections  of 
the  apparatus  and  write  a  brief  statement  of  the  steps  of 
the  experiment.  Include  in  the  description  any  observed 
facts  not  already  noted  in  the  table. 

Discussion : 

Lead  peroxide  is  chocolate  colored.  Which  plate,  the 
lead  or  the  lead  peroxide,  is  the  positive  plate  when  the 
cell  is  charged  ?  Does  the  cell  store  electricity  or  chemical 
energy  which  can  be  converted  into  electricity  ? 

Conclusion : 

State  the  action  which  takes  place  in  charging  and  in 
discharging  a  storage  cell. 


EXPERIMENT    73 

Laws  of  Resistance 

OBJECT.  To  determine  how  the  resistance  of  a  wire  is  related 
to  its  length,  area  of  cross  section,  and  material. 

APPARATUS.  Resistance  board,  on  which  are  stretched  the 
following  wires,  connected  in  series :  2  meters  ft  28  copper ;  2 
meters  ft  28  copper ;  2  meters  ft  22  copper ;  4  meters  ft  28 
iron ;  battery  furnishing  about  6  volts ;  low-range  voltmeter  and 
ammeter,  or  d'Arsonval  and  tangent  galvanometers;  ft  18  insu- 
lated wire  for  connections. 

Introductory : 

There  is  a  difference  in  the  filaments  of  a  16  candle 
power  lamp  and  a  32  candle  power  lamp,  made  for  use  at 
the  same  voltage.  The  filament  of  the  more  powerful 
light  allows  about  twice  as  much  current  to  pass  as  the  16 


256 


LABORATORY   EXERCISES 


candle  power  filament  does.  This  difference  in  current  is 
due  to  a  difference  in  the  resistance  of  the  two  filaments. 
The  difference  in  resistance  is  secured  by  making  the  fila- 
ment of  different  dimensions.  With  the  same  number  of 
volts  applied,  a  copper  wire  will  permit  a  greater  current 
to  pass  than  a  German  silver  wire  of  the  same  dimensions. 
Here  it  is  the  material  that  makes  the  difference  in  resist- 
ance. By  experimenting  with  wires  of  known  lengths, 
areas,  and  materials,  the  effect  of  each  of  these  on  the  re- 
sistance of  the  wire  may  be  determined. 

Experimental : 

The  wires  to  be  tested  are  mounted  on  a  board,  provided 
with  binding  posts  at  the  end  of  each  wire.  By  connecting 
a  battery  to  the  two  outside  binding  posts,  a  current  is 


Fig.  91.     A,  2  meters  copper  #28  ;  B,  2  meters  copper  #28 ;    C,  2  meters 
copper  #22;  D  4  meters  iron  #28. 

sent  through  the  wires  in  series.  In  order  to  read  the 
value  of  the  current,  an  ammeter  is  inserted  between  the 
battery  and  the  resistance  board.  A  voltmeter  is  provided 
with  wires  which  can  be  connected  to  any  pair  of  binding 


LAWS  OF  RESISTANCE 


257 


posts  (Fig.  91).  The  length  in  meters  of  each  wire  and 
its  area  in  circular  mils  will  be  marked  on  the  board  or 
may  be  measured.  A  circular  mil  is  a  circle  whose 
diameter  is  one  one-thousandth  of  an  inch.  The  area  of 
$  28  wire  is  approximately  160  circular  mils  and  the  area 
of  $  22  wire  is  approximately  640  circular  mils. 

After  the  connections  have  been  made  as  just  described, 
the  current  through  the  wire  and  the  drop  of  potential 
between  the  ends  are  read  and  recorded  in  each  of  the 
following  instances  : 

(a)  2  meters  of  #  28  copper  wire. 
(6)  4  meters  of  $  28  copper  wire. 
(<?)  2  meters  of  $  22  copper  wire. 
(cT)  4  meters  of  #  28  iron  wire. 


OBSERVATIONS 


TRIAL 

LENGTH  OP 
WIRE 

AREA  OF 
WIRE 

MATERIAL 

CURRENT 

PRESSURE 

a 

m. 

c.m. 

copper 

amp. 

V. 

b 

m. 

c.m. 

copper 

amp. 

V. 

c 

m. 

c.m. 

copper 

amp. 

V. 

d 

m. 

c.m. 

iron 

amp. 

V. 

A  diagram  should  be  made  showing  the  connections  of 
the  apparatus,  and  a  brief  description  of  the  method  of  the 
experiment  should  follow  the  table  of  observations. 

By  comparing  the  results  of  (a)  and  (5)  the  effect  of 
length  on  resistance  may  be  obtained  ;  (a)  and  (<?)  will 
show  the  effect  of  area  of  cross  section.  The  resistances 
obtained  in  (6)  and  (d)  will  show  the  comparative  resist- 
ances of  copper  and  iron.  The  resistances  may  be  calcu- 
lated by  the  application  of  Ohm's  Law. 


258  LABORATORY  EXERCISES 

CALCULATED  RESULTS 

Trial  abed 

Kind  of  wire 

Resistance 

Discussion : 

Explain  the  method  of  calculating  the  resistance  of  the 
wires. 

Conclusion : 

State  the  relation  between  the  resistance  of  a  conductor 
and  its  length ;  the  relation  between  the  resistance  and 
the  area  of  cross  section. 

How  many  times  is  the  resistance  of  iron  as  great  as 
that  of  copper  ? 

EXPERIMENT    74 

Effect  of  Temperature  on  Resistance 

OBJECT.  To  observe  the  change  in  resistance  of  various  con- 
ductors with  a  change  in  temperature. 

APPARATUS.  Coil  of  iron  wire,  wound  on  a  porcelain  insulat- 
ing tube  ; 1  similar  coils  of  German  silver  wire  and  of  some  wire  of 
very  low  temperature  coefficient,  such  as  manganin,  or  "  la  la  " ; 
ammeter,  or  low  resistance  galvanometer  ;  iron  tripod  for  support- 
ing coils ;  Bunsen  burner  with  wing  top ;  wire  for  connections ; 
3  storage  cells. 

1  The  porcelain  insulating  tubes  can  be  obtained  from  any  dealer  in 
electrical  supplies ;  binding  posts  are  mounted  on  the  ends  of  wooden 
plugs  inserted  in  the  ends  of  the  tube,  and  the  wire,  wound  tightly 
around  the  porcelain,  is  clamped  between  the  binding  post  and  the  wood. 
(Fig.  92.)  la  la  wire  can  be  purchased  of  H.  Boker  and  Co.,  101  Duane 
St.,  N.Y. ;  manganin  wire  is  sold  by  the  Central  Scientific  Co.,  Chicago. 


EFFECT  OF  TEMPERATURE  ON   RESISTANCE      259 


Fig.  92.    Coil  wound  on  Tube. 


Introductory : 

The  temperature  of  the  conductors  in  the  field  and  in 
the  armature  of  a  dynamo  is  higher  than  that  of  the  sur- 
rounding air  when  the  ma- 
chine is  running  at  full  load. 
Will  they  have  the  same 
resistance  as  at  ordinary 
temperatures  ?  Can  we,  by 
measuring  the  resistance  of  a  cold  incandescent  lamp, 
determine  how  much  current  the  lamp  would  take  at  the 
voltage  necessary  to  make  the  lamp  glow  brightly  ?  Do 
all  conductors  behave  alike  with  regard  to  the  effect  of 
temperature  on  their  resistance  ?  These  are  some  of  the 
questions  which  this  experiment  is  designed  to  answer. 

Experimental : 

(a)  Support  the  coil  of  iron  wire  on  a  tripod,  in  such 
a  way  that  a  considerable  part  can  be  heated.  Arrange  a 
circuit  having  the  coil  of  iron  wire,  the  battery  and  the 
ammeter  in  series.  Observe  and  record  the  reading  of  the 
ammeter.  Place  the  lighted  burner  under  the  central  part 

of  the  coil  and  take  another 
reading  of  the  ammeter  when 
the  coil  becomes  red-hot 
(Fig.  93). 

(5)  Using  the  same  source 
of  current,  read  the  current 
through  the  coil  of  German 
silver  wire,  cold  and  hot. 
(c)    Take  the  same  read- 


Fig.  93. 


ings  with  the  coil  of  special  resistance  wire,  the  name  of 
which  will  be  given  you  by  the  instructor.1 

1  If  it  is  desired  to  extend  the  experiment  to  carbon,  the  resistance  of 
an  incandescent  lamp  can  be  found  when  cold,  by  means  of  a  Wheatstone 


260 


LABORATORY  EXERCISES 
OBSERVATIONS 


TRIAL 

MATERIAL 

TEMPERATURE 
(Hot  or  Cold) 

CURRENT 

a 

Iron 

Cold 

.  amp. 

a 

Iron 

Hot 

.  _  _.amp. 

b 

b 

German  silver 
German  silver 

Cold 
Hot 

amp. 
.  amp. 

c 

Cold 

amp. 

c 

Hot 

amp. 

Make  a  simple  drawing,  showing  one  of  the  coils  being 
heated,  with  the  ammeter  and  battery  connected  in  circuit. 
A  brief  description  of  the  experiment  should  accompany 
the  drawing. 

Record  in  tabular  form,  at  the  top  of  the  right-hand 
page,  whether  the  resistance  of  each  material  is  increased 
or  decreased  by  an  increase  of  temperature.  Remember 
that,  with  the  same  voltage  applied,  an  increase  in  current 
means  a  decrease  in  resistance. 

DEDUCTIONS 

An  increase  of  temperature the  resistance  of  iron. 

An  increase  of  temperature the  resistance  of  Ger- 
man silver. 
An  increase  of  temperature the  resistance  of 

Discussion : 

Metals  in  general  behave  like  iron. 

Account  for  the  fact  that  a  tungsten  lamp  takes  sev- 
eral times  as  much  current  at  the  instant  when  the  current 
is  turned  on  as  it  does  a  few  seconds  later.  Why  is  the 


bridge  ;  and  then  at  normal  voltage  by  the  voltmeter  and  ammeter  method. 
If  this  is  done,  the  results  should  be  recorded  in  a  separate  table. 


INTERNAL  RESISTANCE  OP  A  CELL  261 

special  resistance  wire  which  you  have  tested  better  for  use 
in  a  resistance  box  than  German  silver  ? 

Conclusion : 

What  is  the  effect   of  an  increase  in  temperature  on 
the  resistance  of  most  metals? 


EXPERIMENT  75 

Internal  Resistance  of  a  Cell 

OBJECT.  To  determine  the  effect  of  the  size  of  the  plates  and 
the  distance  between  them  on  the  internal  resistance  of  a  cell. 

APPARATUS.  Tumbler  ;  porous  cup  ;  amalgamated  zinc  ;  cop- 
per plate;  porcelain  top  for  holding  plates  so  that  their  distance 
can  be  varied;  voltmeter;  ammeter;  f  18  insulated  copper  wire 
for  connections. 

MATERIAL.  Dilute  sulphuric  acid  (1:20);  copper  sulphate 
solution. 

Introductory : 

Dry  cells  and  other  cells  are  made  in  different  sizes. 
It  is  natural  to  suppose  that  there  is  some  difference  in 
the  performance  of  one  of  the  three  tiny  cells  contained 
in  a  pocket  flash  lamp,  and  one  of  the  large  dry  cells  used 
for  ignition  in  an  automobile.  By  using  a  cell  in  which 
the  area  of  the  plates  immersed  and  the  distance  between 
them  can  be  varied,  we  can  determine  what  effect  the  size 
and  distance  of  the  plates  has  on  the  voltage  and  on  the 
amperage  of  the  cell. 

Experimental : 

From  the  materials  furnished  you,  assemble  a  Daniell 
cell.  The  distance  between  the  plates  of  your  cell  may  be 


262 


LABORATORY  EXERCISES 


varied  by  moving  the  clamps  which,  hold  the  plates  toward 
or  away  from  each  other.  This  will  change  the  length  of 
the  liquid  conductor  by  which  the  current  flows  through 
the  cell,  without  changing  its  cross  section.  The  cross 
section  of  the  liquid  conductor  depends  upon  the  area  of 
the  plates  immersed  in  the  electrolytes,  and  may  be 
changed  without  varying  the  length.  The  materials  of 
the  conductor  remain  unchanged  throughout. 

Except  when  taking  readings,  keep  the  circuit  open. 
The  terminals  of  the  cell  should  be  connected  to  one  in- 
strument only  at  a  time,  and  not  to  both. 

(1)  Immerse  the  plates  as  far  as  possible,  and  bring 
them  as  near  together  as  the  walls  of  the  porous  cup  will 
permit.   •  Read  the  voltmeter  and  ammeter  separately  and 
record  in  the  table  of  observations. 

(2)  Separate  the  plates  as  far  as  the  walls  of  the  tum- 
bler will  permit.     Take  and  record  the  reading  of  each 
instrument. 

(3)  Keeping  the  plates  at  the  same  distance  as  in  (2), 
raise  them  until  the  plates  project  only  1  cm.  into  the 
liquids.     Read  and  record  as  before. 

OBSERVATIONS 


TRIAL 

POSITION  OF  PLATES 

LENGTH  OF  PLATES 

VOLTS 

AMPERES 

1 

Close 

Entire 

2 

Separated 

Entire 





3 

Separated 

1  cm. 





Make  simple  sectional  drawings  of  the  cell,  showing  the 
position  of  the  plates  and  the  amount  immersed  for  each 
case.  A  very  brief  description  should  accompany  these 
drawings. 


GROUPING  OF  CELLS  263 

Discussion : 

Does  the  electromotive  force  of  the  cell  depend  upon 
the  materials  or  upon  the  length  of  the  liquid  conductor  ? 
Upon  what  conditions  does  the  current  furnished  de- 
pend ?  Will  a  large  Daniell  cell  have  a  higher  electro- 
motive force  than  a  small  one  ?  Will  it  furnish  more 
current  ? 

Conclusion : 

Applying  Ohm's  Law,  state  how  the  resistance  of  a  cell 
is  affected  by  the  size  of  the  plates  and  by  the  distance 
between  them. 


EXPERIMENT  76 

Grouping  of  Cells 

OBJECT.  To  determine  the  proper  connection  of  two  cells  to 
secure  the  greatest  current,  (a)  when  the  external  resistance  is  low ; 
(&)  when  the  external  resistance  is  high. 

APPARATUS.  Two  student's  Daniell  cells,  tumbler  form;  resist- 
ance box ;  connection  board,  with  switches  and  connections  as 
shown  in  Fig.  94  (double  connectors  may  be  substituted  for 
switches  if  necessary) ;  ammeter. 

Introductory : 

If  two  like  pumps  are  placed  side  by  side,  drawing  water 
from  the  same  reservoir  and  delivering  into  the  same 
pipe,  the  two  pumps  will  deliver  twice  as  much  water  as 
one  pump  can  deliver,  but  at  the  same  pressure.  These 
pumps  may  be  said  to  be  in  parallel.  If,  however,  the 
two  pumps  were  so  placed  that  the  second  took  its  water 
from  a  pipe  to  which  it  had  been  delivered  by  the  first, 
the  amount  of  water  delivered  would  be  no  greater  than 


264 


LABORATORY   EXERCISES 


that  delivered  by  one  pump,  but  the  pressure  of  the  water 
would  be  twice  as  great.  These  pumps  may  be  spoken  of 
as  in  series. 

Voltaic  cells  may  be  arranged  either  in  parallel  or  in 
series.  The  arrangement  which  will  yield  the  greater 
current  depends  upon  the  external  resistance,  as  compared 
with  the  combined  resistance  of  the  cells.  By  using  a 
low  external  resistance  and  a  high  external  resistance, 
with  the  cells  connected  in  each  of  the  two  ways,  a  gen- 
eral conclusion  may  be  reached. 

Experimental : 

(a)  Two  small-sized  Daniell  cells  are  set  up.  By  the 
use  of  a  combination  of  switches,  as  shown  in  Fig.  94,  or 
by  the  use  of  simple  connecting  wires,  the  zinc  of  one  cell 
is  connected  to  the  copper  of  the 
other.  The  resistance  box  and 
the  ammeter  are  connected  in 
series  with  the  two  remaining 
terminals.  After  making  the 
connections,  inspect  them  to  see 
that  all  the  current  must  pass 
through  each  part  of  the  circuit ; 
this  is  the  test  of  a  series  con- 
nection. Withdraw  the  0.2-ohm 
plug  from  the  resistance  box. 
Read  the  ammeter  and  record  in 
the  table  of  observations  placed 
near  the  top  of  the  left-hand  page. 
Replace  the  0.2-ohm  plug,  and, 
without  changing  connections,  remove  the  20-ohm  plug. 
Read  the  ammeter  and  record. 

(6)  Connect  the  two  copper  plates  and  connect  the  two 
zinc  plates.  To  the  combined  copper  terminal  connect 


Fig.  94. 


GROUPING  OF  CELLS  265 

the  +  terminal  of  the  ammeter,  and  then  connect  the  re- 
sistance box  between  the  other  terminal  of  the  ammeter 
and  the  combined  zinc  terminal  of  the  cells.  Be  sure  that 
the  coppers  of  the  cells  have  no  other  connection  with  the 
zincs,  except  through  the  ammeter  and  resistance  box. 
The  cells  are  now  connected  in  parallel  with  each  other 
and  are  sending  a  current  through  the  resistance  box,  and 
the  same  current  through  the  ammeter.  Take  readings 
through  the  0.2-ohm  coil  and  through  the  20-ohm  coil, 
and  record,  as  in  (a). 

OBSERVATIONS 

CONNECTION  OF  CELLS    SERIES  SERIES  PARALLEL  PARALLEL 

Resistance   ohms    ohms    ohms    ohms 

Current       amp.     amp.    amp.    amp. 

Make  two  connection  diagrams,  one  showing  the  cells 
in  series  connected  with  the  resistance  box  and  ammeter, 
and  the  other  showing  the  cells  in  parallel  connected  with 
the  resistance  box  and  ammeter.  A  brief  description 
should  accompany  the  diagrams. 

Discussion : 

As  the  resistance  of  electrical  apparatus  is  in  general 

much    higher   than    the   battery   furnishing   the  current 

would  have  in  either  arrangement,  which  will  be  the 
usual  method  of  connecting  voltaic  cells  ? 

Conclusion : 

With  what  kind  of  external  resistance  do  cells  in  par- 
allel furnish  the  greater  current?  With  what  kind  of 
external  resistance  are  cells  in  series  better? 


266  LABORATORY  EXERCISES 


EXPERIMENT    77 

Resistance  and  Current  in  a  Divided  Circuit 

OBJECT.  To  compare,  (a)  the  currents  in  the  branches  of  a 
divided  circuit  with  the  resistance  of  those  branches ;  (&)  the  total 
resistance  with  the  resistance  of  the  branches. 

APPARATUS.  Lamp  board  like  that  shown  in  Fig.  95  l ;  32 
candle  power  lamps  to  fill  board;  3  ammeters;  voltmeter,  with 
connecting  wires  ;  connections  to  1 10  volt  D.C.  circuit. 

Introductory : 

In  the  shunt  dynamo  the  current  generated  in  the 
armature  divides,  part  of  it  passing  through  the  coils  of 
the  field  magnet,  and  the  remainder  passing  out  to  the 
external  circuit.  In  the  most  common  type  of  ammeter, 
nearly  all  the  current  passes  through  a  shunt,  connected 
across  the  terminals  of  the  galvanometer  movement,  and 
only  a  small  fraction  passes  through  the  movement  itself. 
In  these  and  other  cases  of  divided  circuits,  or  shunts,  two 
questions  arise  :  How  does  the  current  divide  between 
the  two  paths  ?  What  is  the  combined  resistance  of  the 
paths  ? 

Experimental : 

Proper  connections  for  a  circuit  of  two  branches,  like 
that  shown  in  Fig.  95,  are  to  be  made.  The  resistance  in 

1  The  lamps  may  be  replaced  by  resistance  boxes  and  the  ammeters  by 
tangent  galvanometers,  if  only  part  (a)  of  the  object  of  the  experiment  is 
to  be  worked  out. 


DIVIDED  CIRCUIT 


267 


each  branch  of  the  circuit  consists  of  an  equal  number  of 
similar  incandescent  lamps,  connected  in  parallel.  The 
ammeters  are  so  connected  that  the  total  current  through 
both  branches  can  be  read  and  also  the  individual  current 
in  each  branch.  The  terminals  of  a  voltmeter,  which  is 
not  shown,  are  to  be  connected  to  the  terminals  of  any 
portion  of  the  circuit  whose  resistance  is  desired. 

All  the  lamps  on  both  sides  are  to  be  turned  on  and 
reading   of  each   ammeter  recorded.     The  voltmeter   is 


,()()()()()     ' 

r   ()()()()()     ', 

@ 

Fig.  95.     Lamp  Board,  Ammeters,  and  Connections. 

then  connected  in  succession  to  the  terminals  of  each 
branch  circuit  and  to  the  terminals  of  the  combined  cir- 
cuit and  the  readings  obtained  recorded  in  tabular  form 
near  the  top  of  the  left-hand  page.  All  the  lamps  but 
one  on  one  branch  are  then  turned  out,  leaving  all  the  lamps 
in  the  other  branch  of  the  circuit  burning.  Readings  of 
the  voltmeter  and  ammeters  are  taken  and  recorded  as  be- 
fore. Make  the  following  additional  combinations  in  the 
two  branches  and  record  the  results  :  2  lamps  and  3  lamps  ; 
2  lamps  and  4  lamps  ;  2  lamps  and  5  lamps. 


268 


LABORATORY  EXERCISES 
OBSERVATIONS 


BBANCH  A 

BRANCH  B 

TOTAL  CIRCUIT 

Lamps 

Amperes 

Volts 

Lamps 

Amperes 

Volts 

Amperes 

Volts 

5 
5 
2 
2 
2 





5 

1 
3 
4 

5 

A  simple  diagram  of  connections  should  be  made,  and  a 
brief  description  of  the  method  of  making  the  tests  should 
be  given. 

From  the  readings  of  the  instruments  the  resistance  of 
each  branch  and  the  resistance  of  th.e  entire  circuit  should 
be  calculated  for  each  case,  by  the  application  of  Ohm's 
Law.  The  reciprocal  of  each  resistance  obtained  should 
also  be  calculated  to  four  decimal  places. 


CALCULATED  RESULTS 


Branch  A 

Lamps 
Resistance 


Branch  B 

Lamps  5 

Resistance  (.R&) 


RESISTANCE  BY  SUBSTITUTION  269 


Total  Circuit 
Resistance 
I 
R 


Discussion  : 

Does  increasing  the  number  of  lamps  in  parallel  in  a 
circuit  increase  or  decrease  the  resistance  of  the  circuit?' 
When  a  number  of  equal  known  resistances  are  connected 
in  parallel,  give  a  rule  for  finding  the  combined  resistance. 

Conclusion  : 

(a)  Complete  the  following  statement  : 

The  currents  in  the  branches  of  a  divided  circuit  are 
-----------------  to  the  resistances  of  the  branches  in  which 

they  flow. 

(6)  Compare  -the  sum  of  the  reciprocals  of  the  resist- 
ances of  the  branches  of  the  circuit  with  the  reciprocal  of 
the  resistance  of  the  entire  circuit. 


EXPERIMENT   78 

Resistance  by  Substitution 

OBJECT.  To  determine  the  resistance  of  a  coil  by  direct  com- 
parison with  a  known  resistance. 

APPARATUS.  Galvanometer  ; l  resistance  box  ;  reversing  key 
(Fig.  97)  ;  Daniell  cell,  or  dry  cell ;  two  resistance  coils,  or  other 
resistances,  about  50  to  60  ohms  ;  copper  wire  for  connections. 

JIf  a  d'Arsonval  galvanometer  is  used,  it  should  be  protected  by  4 
shunt  or  by  a  series  resistance. 


270 


LABORATORY  EXERCISES 


Introductory : 

One  of  the  simplest  methods  of  measuring  an  unknown 
resistance  is  by  direct  comparison  with  a  known  resistance. 
When  the  same  voltage  is  applied,  the  currents  in  two 
circuits  will  be  the  same  if  the  resistances  are  equal.  The 
strength  of  two  currents  may  be  compared  by  the  amounts 
that  they  deflect  the  needle  of  a  galvanometer. 

After  reading  the  deflection  of  the  galvanometer  when 
the  unknown  resistance  is  in  circuit,  various  known  resist- 
ances may  be  substituted  for  the  unknown  until  the  same 
deflection  of  the  needle  is  obtained  as  with  the  unknown 
resistance.  As  the  only  difference  in  the  two  circuits  lies 
in  the  resistance  (unknown  or  known)  inserted,  equal  de- 
flections mean  that  a  known  resistance  has  been  inserted 
which  is  equal  to  the  unknown  resistance. 

Experimental : 

Arrange  the  apparatus  as  in  Fig.  96.     J^\^  is  a  re- 
versing key  (Fig.  97).     The  directions  for  the  use  of  galva- 
nometers on   pages  13  and  14 
should  be  read  before  using  the 
instrument. 

(a)  Close  the  key  K±  so  that 
the  current  shall  pass  through 
the  unknown  resistance.  Gently 
tap  the  galvanometer  and  read 
the  deflection.  Immediately 
open  the  key. 


Fig.  96. 


Close  the  key  K%,  so  that  the  current  passes  through 
the  resistance  box,  from  which  one  of  the  plugs  has  been 
removed.  Why  ?  Remove  plugs  so  as  to  obtain  a  total 
resistance  which  will  give  a  deflection  equal  to  that  ob- 
tained with  the  unknown  resistance,  so  far  as  the  range  of 
your  box  will  permit.  Keep  the  key  depressed  only  when 


RESISTANCE   BY  SUBSTITUTION  271 

taking  readings,  and  tap  the  galvanometer,   as   directed 
above. 

Again  connect  the  galvanometer  to  the  unknown  resist- 
ance. If  the  reading  is  not  the  same  as  before,  try  to 
get  a  closer  adjustment  of  the  resistance  box.  Record 
the  final  readings  of  the  gal-  v  ^  ^  , 

vanometer,  connected  through        J^^p«^-w^>_*<^^ll 

the  known  and    through   the          

Fig.  97.     Reversing  Key. 
unknown  resistances. 

(6)  Determine  in  a  similar  way  the  value  of  a  second 
unknown  resistance. 

OBSERVATIONS 

PART  A  PART  B 


Deflection  with  unknown  resistance       .     

Total  known  resistance  in  ohms  .     .     .      

Deflection*  with  known  resistance     .     .     

Make  a  drawing  showing  the  arrangement  of  the  appa- 
ratus, and  describe  with  reference  to  it  the  experimental 
method.  State  also  the  precautions  to  be  observed  with 
regard  to  the  galvanometer  and  its  readings. 

Discussion : 

Why  is  the  circuit  kept  open,  except  when  readings  are 
being  taken  ?  When  the  resistance  box  is  in  circuit, 
should  the  first  resistance  inserted  be  a  large  one  or  a 
small  one?  Explain.  State  why  a  repeated  comparison 
is  made  of  the  readings  of  the  galvanometer  through  the 
known  and  through  the  unknown  resistance. 

Conclusion : 

The  resistance  of is  ohms  ; 

that  of  ..  ..  is   .  ..  ohms. 


272 


LABORATORY   EXERCISES 


EXPERIMENT   79 

Heating  Effect  of  an  Electric  Current 

OBJECT.  To  measure  the  number  of  calories  of  heat  furnished 
by  an  incandescent  lamp  and  to  calculate  the  cost. 

APPARATUS.  Calorimeter  ;  thermometer  ;  1 6  candle  power 
incandescent  lamp  ;  porcelain  keyless  socket ;  voltmeter  ;  amme- 
ter ;  source  of  1 10-volt  current ;  graduate,  or  balance  and  weights  ; 
flexible  insulated  wire  for  connections ;  watch  or  clock  with  sec- 
ond hand. 

Introductory : 

Electrical  heating  devices  are  widely  advertised  and 
many  of  them  extensively  used  on  account  of  their  con- 
venience. The  common  feature  of  them  all  is  a  well- 
insulated  conductor  of  comparatively  high  resistance, 
made  of  a  material  capable  of  being 
heated  to  a  high  temperature  with- 
out melting.  The  incandescent  lamp 
has  these  properties  and  is  sometimes 
used  for  heating  purposes  in  "  lumi- 
nous radiators."  By  allowing  a  lamp 
to  heat  a  known  weight  of  water  for 
a  measured  time,  we  may  find  the 
calories  per  second  furnished  by  the 

1 1     j •    lamp.     If  we  know  the  current  and 

^*  voltage  of  the  lamp,  we  may  estimate 

^)  the  heat  liberated  per  kilowatt  hour. 

Although  all  the  heat  liberated  by 
the  lamp  will  not  be  measured  in 
this  experiment,  yet  the  efficiency  of  the  lamp  as  a  heater, 
as  used  here,  compares  favorably  with  regular  electrical 
heating  apparatus. 


Fig.  98. 


HEATING  EFFECT  OF  AN  ELECTRIC  CURRENT     273 


Experimental : 

A  porcelain  keyless  socket  is  connected  to  a  110-volt 
line,  with  an  ammeter  between  the  socket  and  the  110-volt 
terminals  (Fig.  98).  A  voltmeter  is  connected  across  the 
terminals  of  the  socket.  A  lamp  is  then 
screwed  into  the  socket  and  the  switch 
closed  in  the  circuit  to  make  sure  that  the 
connections  are  correct  and  that  the  in- 
struments read  in  the  proper  direction. 
The  lamp  is  then  turned  off  till  needed. 

Into  a  nickel-plated  brass  calorimeter 
is  placed  250  grams  (cm.3)  of  water  at  a 
temperature  six  or  seven  degrees  below 
room  temperature.1  This  is  stirred 
thoroughly  with  a  thermometer  and  the 
temperature  noted  ;  immediately  the  cur- 
rent is  turned  on  through  the  lamp  which 
is  inserted  in  the  calorimeter,  the  exact 
time  in  minutes  and  seconds  being  noted.  The  time  and 
the  temperature  of  the  water  are  recorded  in  the  tabular 
form  near  the  top  of  the  left-hand  page,  the  voltmeter  and 
ammeter  also  being  read  and  their  readings  recorded.  The 
lamp  should  be  immersed  until  the  tip  rests  on  the  bottom 
of  the  calorimeter,  and  the  thermometer  should  stand  in 
the  calorimeter  beside  the  lamp  (Fig.  99).  For  the  next 
five  minutes  the  lamp  burns  inverted  in  the  water.  By 
moving  the  lamp  up  and  down  in  the  water,  never  raising 
it  more  than  a  quarter  of  an  inch  from  the  bottom,  the 
water  can  be  kept  stirred  and  so  of  equal  temperature 

1  This  is  the  correct  amount  of  water  for  the  ordinary  size  calorimeter. 
The  water  should  reach  to  within  a  quarter  of  an  inch  of  the  metal  base 
of  the  bulb,  when  the  latter  is  completely  immersed.  If  the  calorimeter 
is  large  enough  to  permit  the  use  of  a  larger  lamp,  it  should  be  used  and 
the  amount  of  water  adjusted  as  just  stated. 


Fig.  99. 


274 


LABORATORY   EXERCISES 


throughout.  The  calorimeter  should  not  be  handled  dur- 
ing the  experiment.  The  voltmeter  and  ammeter  should 
be  frequently  observed,  aijd  if  there  is  any  variation,  the 
average  reading  for  the  whole  time  .should  be  the  one 
recorded  and  used. 

When  the  lamp  has  been  in  the  water  exactly  five  min- 
utes, take  it  out  promptly,  stir  the  water  vigorously  with 
the  thermometer,  and  read  and  record  the  temperature. 

Using  fresh  quantities  of  water,  repeat  the  test  twice. 
The  water  equivalent  of  the  calorimeter  should  be  obtained 
from  the  instructor. 


OBSERVATIONS 


TRIAL 

TIME 

TEMPEBATI:RE 

VOLTS 

A.MPEKE8       . 

Begin 

End 

Begin 

End 

Begin 

End 

Begin 

End 

1 
o 

3 

Weight  of  water 

Water  equivalent  of  calorimeter 


Make  a  sectional  drawing  of  the  calorimeter  with  lamp 
and  thermometer  in  place  and  with  the  connections  of 
the  instrument  shown.  A  brief  description  of  the  method 
of  the  experiment  should  accompany  the  drawing. 

From  the  weight  of  the  water,  with  the  water  equiva- 
lent of  the  calorimeter  added,  and  the  change  of  tempera- 
ture, the  number  of  calories  furnished  in  five  minutes  can 
be  calculated.  The  number  of  watt-seconds  is  found  by 
multiplying  volts,  amperes,  and  seconds  together.  From 
these  two  results  calculate  the  calories  per  watt-second 


HEATING  EFFECT  OF  AN  ELECTRIC  CURRENT     275 

and  per  kilowatt  hour.  As  the  time  and  the  weight  of 
water  are  the  same  in  all  three  tests,  the  averages  of  tem- 
perature changes,  volts,  and  amperes  will  be  used  in  the 
calculation.  The  problem  called  for  in  the  conclusion 
should  be  worked  out  in  the  note-book,  using  the  local  rate 
for  electricity. 

CALCULATED  RESULTS 

Corrected  weight    of    water  (water  -\-  water 

equivalent  of  calorimeter) g. 

Average  temperature  change  in  five  minutes    .  °C. 

Calories  furnished  in  five  minutes    ....  cal. 

Calories  furnished  per  second cal. 

Watt-seconds  of  energy  used  in  five  minutes    .  w.s. 

Calories  per  watt-second 

Calories  per  kilowatt  hour 

Cost  of  current  per  kilowatt  hour      ....  cts. 

Discussion : 

Explain  any  way  in  which  heat  generated  by  the  lamp 
may  escape  without  being  measured  in  this  experiment. 

Conclusion : 

At  the  price  of cents  per  kilowatt  hour,  the  cost  of 

raising  4  liters  of  water  from  15°  C.  to  100°  C.  will  be 

cents,  if  an  electric  heater  of  the  same  efficiency  as  the 
lamp  is  employed. 


276  LABORATORY   EXERCISES 

EXPERIMENT    80 

Study  of  an  Incandescent  Lamp 

OBJECT.  To  measure  the  current,  voltage,  resistance,  and  power 
consumption  of  an  incandescent  lamp. 

APPARATUS.  Lamp  socket,  mounted  on  block  with  two  bind- 
ing posts  connected  to  the  socket ;  1 6  and  32  candle  power  in- 
candescent lamps  ;  low-range  ammeter ;  120-volt  voltmeter ;  one 
or  more  lamps  with  the  metal  cap  removed ;  at  least  one  tung- 
sten lamp,  of  known  candle  power;  $  18  wire  for  connections  to 
source  of  1 10-volt  current. 

Introductory : 

When  we  pay  for  electric  light,  we  desire  to  get  as 
much  as  possible  for  our  money.  We  need  to  know  the 
pressure  required  and  the  current  consumed  by  our  lamps. 
From  these  we  can  calculate  the  resistance  of  the  lamp 
anrj  the  power  in  watts  required  to  light  it.  By  the  use 
of  a  voltmeter  and  an  ammeter 
properly  connected  to  the  lamp, 
we  can  observe  the  pressure  and 
current  directly.  The  resistance 
may  be  calculated  by  applying 
Ohm's  Law.  The  watts  are  equal 
to  the  volts  multiplied  by  the 
amperes. 

Experimental : 

Connect  the  ammeter  in  series 

with  the  lamp  and  the  source  of 
current.  Connect  the  voltmeter  to  the  terminals  of  the 
lamp  socket,  so  that  it  will  measure  the  fall  of  potential 
through  the  lamp  only.  Readings  are  to  be  made  with 
16  and  32  candle  power  lamps,  and  the  results  worked 


STUDY  OF  AN  INCANDESCENT  LAMP          277 

out  in  each  case.  Readings  with  a  tungsten  lamp  should 
be  made  by  some  members  of  the  class.  The  results  may 
be  entered  by  the  other  members  of  the  class  for  purposes 
of  comparison.  Assuming  the  candle  power  to  be  cor- 
rectly stated  for  the  lamp,  the  number  of  watts  required 
for  each  unit  of  candle  power  of  the  lamp  should  be  cal- 
culated. This  is  known  as  the  efficiency  of  the  lamp,  and, 
since  power  is  what  we  pay  for,  it  is  used  in  comparing 
the  economy  of  different  kinds  of  lamps. 

The  readings  obtained  should  be  recorded  in  tabular 
form  near  the  top  of  the  left-hand  page. 

OBSERVATIONS 

CUBRENT        VOLTAGE 

16  candle  power  lamp      ....  amp.          volts 

32  candle  power  lamp       ....  amp.  volts 

__  candle  power  tungsten  lamp        .          amp.          volts 

A  careful  outline  drawing,  showing  a  vertical  section 
of  the  lamp,  with  the  parts  labeled,  should  be  made,  in 
addition  to  the  diagram  showing  the  connections. 

At  the  top  of  the  right-hand  page  place  the  results 
obtained  by  calculation. 


RESISTANCE  POWER  EFFICIENCY 

watts 


CALCULATED  RESULTS 

RESISTANCE  Po 

16  candle  power  lamp  .          ohms          watts 

32  candle  power  lamp  .          ohms          watts 

c.p. 

Conclusion : 

The  average  efficiency  of  a  carbon  incandescent  lamp 

is wat.tf  ;  of  a  tungsten  lamp  is-.   -  watts.. 

caudle  candle 


278  LABORATORY   EXERCISES 

EXPERIMENT    81 

Lines  of  Force  around  a  Conductor 

OBJECT.  To  investigate  the  magnetic  field  surrounding  a  con- 
ductor. 

APPARATUS.  No.  10  copper  wire,  bent  at  right  angles  and  pro- 
vided with  binding  posts  or  double  connectors  at  the  ends ;  dry 
cell  or  other  source  of  current ;  reversing  switch  ;  $  1 8  insulated 
copper  wire  for  connections ;  4  small  exploring  compasses  ;  2.5 
cm.  compass;  support  which  will  permit  the  exploring  compasses 
to  be  placed  around  the  vertical  portion  of  the  wire,  while  the 
larger  compass  may  be  placed  either  above  or  beneath  the  hori- 
zontal portion. 

Introductory : 

When  a  current  passes  through  a  wire,  magnetic  effects 
may  be  observed  in  the  vicinity  of  the  wire.  As  such 
effects  are  always  associated  with  the  presence  of  lines  of 
force,  we  wish. to  explore  the  field  around  the  conductor 
to  find  the  direction  of  these  lines.  This  may  easily  be 
done  by  using  compass  needles,  if  we  remember  that  a 
magnetic  compass  will  set  itself  tangent  to  a  line  of  force, 
and  that  a  north  pole  will  point  in  the  direction  of  a  line 
of  force. 

Experimental : 

The  direction  of  the  current  is  from  the  +  terminal  of 
the  cell,  or  dynamo,  to  the  apparatus.  Trace  the  current 
through  the  apparatus  and  back  to  the  —  terminal. 

1  Note  to  Instructor.  The  apparatus  may  be  assembled  permanently  in 
the  form  shown  in  Fig.  101.  The  small  compasses  are  set  in  holes  bored 
in  the  block  with  a  bit  and  cemented  in  place  by  rubbing  them  with  a 
little  shellac  just  before  they  are  set  in  place. 


LINES  OF  FORCE  AROUND  A  CONDUCTOR       279 

(a)  We  may  determine  the  direction  of  the  magnetic 
field  around  a  conductor  passing  vertically  through  a  block 
by  placing  small  compasses   on 
the  block  around  the  wire  and 
observing  their  position,  — 

(1)  when   there   is  no   current 

flowing ; 

(2)  when  the  current  flows  up; 

(3)  when     the     current    flows 

down. 

The  observations  are  to  be 
recorded  in  three  diagrams  at 
the  top  of  the  left-hand  page. 
In  each  diagram  the  position 
taken  by  the  small  needles  is  to  be  shown  by  arrows 
in  the  four  larger  circles.  The  small  circle  in  the  cen- 
ter represents  the  wire.  A  current  flowing  up  (toward 
the  observer)  is  represented  by  a  dot  in  a  circle,  thus  O ; 
a  current  flowing  down  (away  from  the  observer)  by  ®. 
These  signs  represent  respectively  the  point  of  an  arrow 
coming  toward  the  observer  and  the  feathers  of  an  arrow 
going  away  from  him.  A  sample  diagram,  showing  the 
^ — -^  position  of  the  needles  in  one  case, 

is  given  in  Fig.  102. 

(J)  Place  your  apparatus  so  that 
the  horizontal  wire  is  parallel  to  one 
needle  when  no  current  is  flowing. 
Place  the  compass  under  the  wire 
and  turn  on  the  current.  Observe 
the  direction  of  deflection  of  the 
needle  and  record  in  diagrams,  simi- 
lar to  that  shown  in  Fig.  103,  placed  in  the  upper  part  of 
the  rightrhand  page.  Note  beside  each  diagram  the  posi- 


280  LABORATORY  EXERCISES 

tion  of  the  wire  with  respect  to  the  needle  (wire  above  or 
wire  below}.  The  dotted  arrow  indicates  the  original 
position  of  the  needle  before  the  current  passes  and  the 
solid  arrow  the  position  of  the  needle  during  the  passage 
of  the  current.  In  all  representations  of  the  compass 
needle,  the  arrowhead  indicates  the  north  pole. 

Observe  and  record  in  the  manner  just 
described  the  four  following  cases  : 

(1)  Current  S  to  N,  wire  over  needle  ; 

(2)  Current  N  to  S,  wire  over  needle  ; 

(3)  Current  S  to  N,  wire  under  needle ; 

(4)  Current  N  to  S,  wire  under  needle. 
Fig.  103. 

A  simple  outline  drawing  of  the  apparatus 

should  be  made  on  the  left-hand  page  immediately  below 
the  diagrams  of  results,  and  a  brief  description  of  opera- 
tions written,  referring  to  the  drawings  and  diagrams.  On 
the  lower  part  of  the  right-hand  page  state  the  conclusions. 

Conclusion : 

(1)  What  is  the  shape  of  the  lines  of  force  around  a 
straight  conductor  ? 

(2)  Imagine  the  current  as  flowing  in  your  right  hand 
toward  the  fingers.     If  the  palm  faces  the  needle,  toward 
what  part  of  the  hand  is  the  needle  deflected  ?     Make  a 
full  statement  of  this  relation. 

(3)  Suppose  the  wire  to  be  grasped  in  the  right  hand, 
with  the  current  flowing  in  the  direction  in  which  the 
thumb   points.     In  what  direction  do  the  lines  of  force 
extend  ?     Make  a  full  statement  of  this  relation. 


THE  ELECTROMAGNET  281 

EXPERIMENT    82 

The  Electromagnet 

OBJECT.  To  study  the  construction  of  the  electromagnet,  and 
to  determine  the  conditions  of  its  operation. 

APPARATUS.1  Three  electromagnet  coils;2  a  good  dry  cell; 
single  contact  key;  small  box  of  half-inch  brads;  ft  18  wire  for 
connections  ;  compass. 

Introductory : 

Doorbells,  telegraph  instruments,  dynamos,  motors,  and 
many  other  kinds  of  electrical  apparatus  depend  for  their 
operation  on  electromagnets.  These  electromagnets  con- 
sist of  coils  of  wire,  or  solenoids,  usually  containing  an 
iron  core.  We  wish  to  locate  the  poles  of  such  a  magnet, 
to  find  the  effect  of  the  iron  core  on  the  strength  of  the 
magnet,  and  to  find  the  effect  of  the  number  of  turns  of 
wire.  Later  experiments  will  take  up  applications  of  the 
electromagnet. 

Experimental : 

(a)  Connect  the  terminals  of  the  coil  wound  on  the 
wooden  core  (Fig.  104,  (7)  to  the  dry  cell  through  the  con- 
tact key.  By  means  of  a  compass  needle,  determine  which 

1  The  authors  are  indebted  to  Mr.  W.  R.  Pyle,  Morris  High  School, 
N.  Y.  City,  for  the  plan  of  this  experiment. 

2  Two  of  the  coils  are  wound  on  ^"  soft  iron  cores  and  the  third  on 
\"  dowel  rod.     The  ends  of  the  iron  cores  should  be  rounded  off,  as 
shown  in  Fig.  104,  to  increase  the  effect.    On  one  of  the  iron  cores  (B)  wind 
100  turns  of  #  22  insulated  wire  ;  the  ends  of  the  coil  are  held  in  place  by 
rubber  rings,  cut  from  a  piece  of  tubing,  with  a  slightly  smaller  internal 
diameter  than  the  rod.     After  winding,  the  magnet  is  dipped  in  shellac, 
to  hold  the  windings  and  rings  in  place.     On  the  wooden  core  an  exactly 
similar  winding  is  placed  and  shellacked.     The  other  iron  core  (.4)  is  simi- 
larly wound,  but  with  60  turns  only. 


282 


LABORATORY   EXERCISES 


end  of  the  coil  acts  like  a  north  pole  and  which  end  like  a 
south  pole.  The  key  should  be  closed  only  when  readings 
are  being  made,  as  otherwise  the  cell  will  rapidly  polarize. 
Trace  the  direction  of  the  current  from  the  positive 
(carbon)  pole  of  the  cell  through  the  coil,  noting  particu- 
larly the  direction  in  which  it  flowed  around  the  coil. 
Record  this  in  the  form  of  a  simple  diagram,  showing  only 

a  very  few  turns  of  wire 
wound  on  the  core,  with 
an  arrowhead  on  each 
to  show  the  direction  of 
the  current,  and  with 
the  poles  marked. 

Grasp  the  coil  in  the 
right  hand,  with  the 
fingers  pointing  around 
it  in  the  direction  of  the 
current  and  the  thumb 
extended.  Does  the 
thumb  point  in  the  direction  of  the  north  pole  or  in  the 
direction  of  the  south  pole  of  the  coil?  State  the  relation 
in  full  in  the  Discussion. 

(5)  Using  the  coil  (Fig.  104,  A)  having  the  smaller 
number  of  turns  wound  on  an  iron  core,  test  for  polarity 
as  in  (a).  Does  the  presence  of  an  iron  core  change  the 
relation  between  the  direction  of  the  current  around  the  mag- 
net and  the  location  of  the  poles? 

Test  the  strength  of  the  electromagnet  by  pushing  one 
end  into  a  box  of  brads,  and  then  closing  the  circuit  and 
removing  the  magnet  with  the  brads  which  stick  to  it. 
Observe  the  behavior  of  the  brads  when  the  circuit  is 
opened.  What  does  this  behavior  indicate  ?  The  brads 
picked  up  by  the  electromagnet  should  be  counted  and 
the  number  recorded. 


Fig.  104. 


THE  ELECTROMAGNET  283 

(c)  Determine  the  number  of  brads  which  can  be  picked 
up  by  the  coil  with  the  larger  number  of  turns  and  the 
iron  core  (Fig.  104,  .5),  and  record.  Count  the  number  of 
turns  on  each  of  the  three  coils.  How  is  the  strength  of  an 
electromagnet  affected  by  the  number  of  turns  of  wire  it  has  ? 

(rf)  Try  to  pick  up  brads  with  the  coil  on  the  wooden 
core,  and  record  the  result.  What  effect  has  the  use  of  an 
iron  core  on  the  strength  of  an  electromagnet  ? 

Record  the  numerical  results  obtained  in  tabular  form 
near  the  top  of  the  left-hand  page. 

OBSERVATIONS 

MATERIAL  OP  COBB  NUMBER  OF  TURNS  NUMBER  OF  BRADS  PICKED  UP 


A  brief  description  of  the  tests  made  should  follow  the 
table  of  observations  and  should  include  such  observed 
results  as  are  not  stated  in  the  table.  A  simple  drawing 
should  be  made,  showing  one  of  the  coils  connected  with 
the  cell  and  key. 

Discussion : 

The  questions  in  italics  in  the  experimental  directions 
should  be  answered  under  this  heading. 

Conclusion : 

State  the  conditions  necessary  for  a  strong  electro- 
magnet. 


284  LABORATORY  EXERCISES 


The  Electric  Bell 

OBJECT.  To  study  the  construction  and  operation  of  the  elec- 
tric bell. 

APPARATUS.  Electric  bell  with  cover  removed ;  dry  cell ;  push 
button;  $  18  wire  for  connections  ;  magnetic  compass.  It  is  de- 
sirable to  bend  the  hammer  rod  so  that  the  hammer  does  not 
actually  strike  the  bell. 

Introductory : 

The  electric  bell  is  one  of  the  most  familiar  applications 
of  the  electromagnet.  A  clear  understanding  of  its  con- 
struction, therefore,  is  of  value  to  enable  us  to  know  what 
may  be  expected  of  the  bell  and  what  adjustments  are 
necessary  when  it  fails  to  operate  properly. 

Experimental : 

(a)  Connect  the  bell,  the  cell,  and  the  push  button  in 
series,  so  that  the  bell  will  ring  when  the  circuit  is  closed 
by  the  push  button. 

(6)  Trace  the  path  of  the  current  through  the  bell, 
starting  at  one  of  the  binding  posts.  What  draws  the 
hammer  toward  the  bell  ?  What  draws  the  hammer  away 
from  the  bell  ? 

(c)  Place  a  compass  needle  near  the  ends  of  the  mag- 
net coils.  Hold  the  armature  against  the  contact  screw. 
Close  the  circuit  and  observe  the  result.  Repeat  with 
the  armature  held  against  the  magnet  poles.  Is  the  mag- 
net stronger  when  the  armature  is  pressed  against  the 
contact,  or  when  it  is  against  the  poles  ? 

(cT)    Detach   the  wire  from  the  binding   post  on  the 


THE  ELECTRIC  BELL 


285 


armature  side  of  the  bell,  and  press  the  end  of  the  wire 
against  the  contact  screw.  Close  the  circuit.  Note  and 
explain  the  difference  in  operation. 

(js)  On  the  right-hand  page,  make  a  full-size  diagram 
of  the  instrument  and  its  connections.  Indicate  by 
arrows  the  direction  of 
the  current  at  each  im- 
portant point. 

Label    the    following 
parts : 

electromagnet  cores 
contact  screw 
spring 

electromagnet  yoke 
vibrating  armature 
push  button. 


—    Battery 


(/)  Examine  a  push 
button  and  determine 
how  the  contact  is  made. 
Below  the  diagram  of 
the  bell,  make  a  sketch 
of  a  vertical  section  of 
the  push  button  and 
show  the  proper  connections  of  battery,  push  button,  and 
bell. 

Discussion : 

Explain  the  results  of  the  tests  in  part  (<?).  Why  is  the 
operation  continuous  when  the  circuit  is  closed  ? 

What  change  in  connections  would  convert  this  into  a 
single-stroke  bell,  in  which  the  gong  is  struck  but  once 
each  time  the  circuit  is  closed  ? 

Make  diagrams  showing  the  connection^  necessary  for 


286  LABORATORY  EXERCISES 

(1)  two  bells  rung  by  one  push  button ;  (2)  two  push 
buttons  used  to  ring  the  same  bell.  Show  the  cell  in 
each  case. 


EXPERIMENT   84 

Telegraph  Instruments 

OBJECT.  To  study  the  construction  and  operation  of  the  instru- 
ments used  on  a  telegraph  line. 

APPARATUS.  Telegraph  key  and  sounder;  dry  cell  or  other 
source  of  current;  ft  18  wire  for  connections  ;  at  least  one  relay, 
properly  connected  in  circuit  with  a  key  and  sounder,  for  the  labo- 
ratory, —  if  possible  one  for  each  laboratory  table ;  compass. 

Introductory : 

Joseph  Henry,  who  made  the  first  electromagnets  in 
this  country,  suggested  the  possibility  of  sending  signals 
to  a  distant  point,  and  fifteen  years  later  Morse  con- 
structed the  first  practical  telegraph  line.  The  telegraph 
is,  therefore,  the  earliest  application  of  the  electromagnet 
and  one  of  the  simplest  and  most  useful  electrical  devices 
that  we  have. 

Experimental :      ^ 

(1)  A  telegraph  key  and  a  sounder,  a  cell,  and  connect- 
ing wires  will  be  furnished  you.     These  are  to  be  con- 
nected in  such  a  way  that  a  current  will  pass  through  the 
sounder  from  the  cell  when  the  key  is  depressed.     After 
satisfying  yourself  that  the  connection  is  properly  made, 
the  circuit  should  not  be  closed  unnecessarily,  as  the  noise 
is  distracting  to  others. 

(2)  Press  the  key;  observe  and  record  the  resulting 
movement  in  the  sounder.     If  the  instructor  so  directs, 


TELEGRAPH  INSTRUMENTS 


287 


produce  a  dot,  a  dash,  and  any  combination  he  may  require, 
under  his  observation. 

(3)    Trace  the  path  of  the  current  through  the  entire 
circuit.      Holding  the  compass  near  the  top  of  one  of 
the  electromagnet  coils, 
determine   whether    the 
magnet  is  stronger  when 
the  key  is  open  or  when 


Fig.  106. 


Insulated 

The  Key. 


it  is  closed.     Account  for 
the  effect  produced  by  clos- 
ing the  key.     Account  for  the  effect  ivhen  the  key  is  opened. 
Operate  the  short-circuit  lever  at  the  side  of  the  key. 

(4)  On  the  upper  half  of  the  right-hand  page,  make 
drawings  of  the  key  and  of  the  sounder,  seen  from  the 
side.  Make  a  simple  diagram  showing  the  arrangement 
of  battery,  key,  sounder,  and  connecting  wires.  Connec- 
tions in  the  instruments  themselves,  which  are  not  exter- 
nally visible,  may  be  indicated  by  dotted  lines.  Mark  the 
following  parts  :  In  the  sounder  —  magnet  coils,  soft  iron 
armature,  locker  arm,  pivot,  spring.  In  the  key  —  lever, 
pivot,  contact  points,  spring.  Indicate  the  position  of  any 
insulating  material.  Show  by  dotted  lines  the  path  of  the 

current  through  base,  pivot, 
and  lever. 

(5)  Examine  the  con- 
struction of  a  relay,  if  one 
is  available.  Trace  the 
connections  in  its  circuits 
and  state  what  connec- 
tions are  made  from  the 


Fig.   107.     The  Sounder. 


outside  to  each  pair  of  binding  posts. 

The  drawings  called  for  in  (4)  should  be  made  first ; 
any  additional  description  of  the  instruments  should  be 
placed  on  the  left-hand  page,  accompanying  a  statement  of 


288  LABORATORY   EXERCISES 

facts  observed  in  the  examination  and  tests  of  the  instru- 
ments. 

Discussion : 

Answer  the  italicized  questions  in  the  experimental 
directions  .as  well  as  the  following : 

Explain  the  use  of  the  side  lever  in  a  line  including  two 
or  more  stations  whose  instruments  are  in  series.  How 
many  keys  can  be  in  use  in  such  a  line  at  a  time  ?  Why? 
Why  can  a  relay  be  operated  by  a  weaker  current  than  a 
sounder  needs  ?  Explain  the  use  of  a  relay  in  a  telegraph 
circuit. 


EXPERIMENT    85 

Operation  of  an  Electric  Motor 

OBJECT,  (a)  To  observe  the  effect  of  a  magnetic  field  on  a  cur- 
rent-bearing conductor ;  (&)  to  study  the  construction  and  operation 
of  an  electric  motor. 

APPARATUS.  Rectangular  loop  of  $  28  spring  brass  wire,  about 
10  inches  long  and  1|  inches  broad  (Fig.  108)  ;  large  U-shaped 
magnet,  like  those  used  in  making  magnetos  or  voltmeters ; 
2  storage  or  dry  cells ;  reversing  switch  ;  4  or  6  volt  motor,  with 
drum-wound  armature,  mounted  so  that  the  connection  of  the 
field  leads  to  the  armature  can  be  reversed  ;  $  1 8  insulated  copper 
wire  for  connections. 

Introductory : 

The  electric  motor  consists  essentially  of  a  coil  of  wire 
(armature)  carrying  a  current,  which  rotates  between  the 
poles  of  an  electromagnet.  A  commutator  on  the  arma- 
ture shaft  keeps  the  current  flowing  in  a  constant  direc- 
tion through  the  armature.  The  wires  on  the  opposite 


OPERATION  OF  AN  ELECTRIC  MOTOR          289 


sides  of  the  armature  are  caused  to  move  by  their  lines  of 
force  seeking  to  become  parallel  with  the  lines  of  force  of 
the  field.  By  passing  a  current,  first  in  one  direction  and 
then  in  the  other,  through  a  pliable  wire  located  in  a  mag- 
netic field,  we  can  imitate  the  action  of  the  two  wires 
forming  the  opposite  sides  of  a  coil  on  the  armature. 

Experimental : 

(a)  Pass  a  current  through  the  loop  of  wire  from  a 
storage  cell  or  dry  cell.  The  circuit  should  be  closed 
only  when  making  tests.  Bring  the  horseshoe  magnet 
into  such  a  position  that  the  loop  will  be  opposite  the 
opening  between  the  poles.  Have  the  north  pole  of  the 
magnet  at  the  top,  so  that  the  magnetic  field  will  be 
downward.  Observe  the  behavior  of  the  wire. 

Make  a  diagram,  showing  by  a  few  lines  of  force  in 
each  case  the  field  due  to  the  magnet  and  that  due  to  the 
current  in  the  loop  of  wire.  Indicate  on 
the  diagram,  by  arrows  properly  placed,  the 
direction  of  the  current,  of  the  lines  of 
force,  and  of  the  motion  of  the  loop.  Re- 
peat the  test,  with  the  direction  of  the  cur- 
rent in  the  loop  reversed.  Record  the  result 
in  another  diagram. 

(by  Connect  the  field  terminals  and  the 
armature  terminals  of  the  motor  furnished, 
thus  making  it  a  shunt  motor.  Next  con- 
nect the  armature  terminals  through  a  re- 
versing switch  to  two  or  more  cells  in  series. 
Close  the  switch,  and  observe  the  direction  of  rotation  of 
the  armature.  Reverse  the  switch  and  again  observe  the 
direction  of  rotation.  Keeping  the  direction  of  the  cur- 
rent in  the  armature  the  same,  change  the  direction  of 
current  through  the  field,  by  reversing  the  connection  of 


Fig.  108. 


290  LABORATORY   EXERCISES 

the  field  terminals.     Observe  the  direction  of  rotation  in 
this  case. 

The  results  of  the  tests  in  part  (a)  are  to  be  recorded 
in  the  two  diagrams,  which  should  be  accompanied  by  a 
brief  description  of  the  operations.  The  results  in  part 
(5)  should  be  stated  in  connection  with  the  description  of 
the  work.  This  description  should  be  accompanied  by  a 
drawing  showing  a  side  view  of  the  motor,  in  which  the 
following  parts  are  shown  and  labeled: 
field  magnet  armature  brushes  commutator 

Discussion : 

Does  this  experiment  illustrate  the  following  rule  for 
the  motor  ?  "  Let  the  forefinger  of  the  left  hand  point  in 
the  direction  of  the  magnetic  field,  and  the  second  finger 
at  right  angles  to  the  forefinger,  in  the  direction  of  the 
current ;  then  the  thumb  will  indicate  the  direction  in 
which  the  current-bearing  conductor  will  move." 

To  reverse  a  motor,  should  both  field  and  armature  con- 
nections be  reversed,  or  only  one  of  them  ? 


EXPERIMENT   86 

Power  and  Efficiency  of  a  Motor 

OBJECT.  To  determine  the  horse  power  developed  by  an  electric 
motor  and  the  efficiency  of  the  motor  when  developing  that  horse 
power. 

APPARATUS.  Electric  motor,  not  smaller  than  \  H.P.,  with 
starting  box  and  proper  connections  to  a  source  of  current ;  canvas 
or  leather  strap,  equal  in  width  to  the  pulley  of  the  motor,  with 
two  spring  balances  of  12  Ib.  capacity;  suspension  bar  for  the  bal- 
ances and  strap,  with  an  upright  support  to  which  it  can  be  clamped 
(Fig.  110);  speed  counter;  watch;  voltmeter  and  ammeter. 


POWER  AND  EFFICIENCY  OF  A  MOTOR        291 

Introductory : 

In  the  selection  of  a  motor,  whether  it  is  to  run  an  auto- 
mobile or  a  sewing  machine,  the  first  consideration  is  to 
secure  one  that  has  the  proper  horse  power.  When  a 
motor  of  the  proper  power  has  been  found,  then  the  effi- 
ciency with  which  it  does  its  work  should  be  investigated. 
Both  the  power  and  the  efficiency  of  a  motor  can  be 
measured  with  very  simple  apparatus. 

To  calculate  the  horse  power,  it  is  necessary  to  find  the 
number  of  foot  pounds  of  work  done  per  minute  and  di- 
vide this  by  33,000,  according  to  the  definition  of  horse 
power.  The  number  of  foot  pounds  can  be  found  by 
measuring  with  a  spring  balance  the  number  of  pounds 
friction  between  the  motor  pulley  and  a  brake  against 
which  it  turns,  and  multiplying  this  result  by  the  total 
number  of  feet  which  a  point  on  the  revolving  pulley  will 
travel  in  one  minute.  The  rated  horse  power  of  a  motor 
or  engine  is  the  power  it  develops  when  working  at  full 
load;  it  does  not  develop  this  power  at  all  times. 

The  efficiency  of  a  machine  is  the  percentage  of  total 
work  done  on  the  machine  which  proves  useful,  or,  since 
power  is  the  rate  of  doing  work,  it  is  the  percentage  of 
total  power  applied  to  the  machine  which  proves  useful. 
By  measuring  the  amperes  of  current  flowing  through  the 
motor  and  the  voltage  applied  to  the  machine,  we  can  cal- 
culate the  power  applied  in  watts.  Since  1  horse  power 
is  equal  to  746  watts,  the  ratio  of  the  power  exerted  by 
the  motor  on  the  brake  and  the  power  applied  to  the  motor 
by  the  current  is  readily  found. 

Experimental : 

The  motor,  voltmeter,  and  ammeter  should  be  connected 
to  a  source  of  current,  as  shown  in  Fig.  109,  according  to 
specific  directions  to  be  given  by  the  instructor.  Unless 


292 


LABORATORY  EXERCISES 


Fig.  109. 


a  starting  box  is  provided,  the  ammeter  terminals  should 
be  short-circuited  by  a  switch,  which  should  not  be  opened 
until  the  motor  has  reached  full 
speed.  If  a  starting  box  is  used, 
the  ammeter  should  be  connected 
between  the  source  of  current  and 
the  starting  box,  so  that  its  read- 
ings shall  show  the  current  taken 
by  both  armature  and  field.  The  voltmeter,  in  any  case, 
should  be  directly  across  the  armature  terminals  of  the 
motor. 

The  brake  consists  of  a  strap,  hung  by  two  spring  bal- 
ances from  an  adjustable  support.  By  raising  this  sup- 
port until  the  bend  in  the  strap  is  held  against  the  under 
side  of  the  motor  pulley  by  the  partly  stretched  springs  of 
the  balances,  a  frictional  force  is  exerted  on  the  surface  of 
the  pulley,  the  amount  of  which  is  equal  to  the  difference 
between  the  readings  of  the  two 
balances. 

The  diameter  of  the  pulley  and 
the  thickness  of  the  belt  in  inches 
should  be  measured  before  the  test 
is  started  and  recorded  in  the  tabu- 
lar form  near  the  top  of  the  left- 
hand  page.  A  speed  counter  and 
watch  should  be  at  hand,  ready  for 
use,  and  the  student  who  is  to  take 
the  speed  should  be  given  specific 
directions  by  the  instructor.  When 
everything  is  ready,  one  student 
should  take  charge  of  the  manage- 
ment of  the  brake  and  reading  of  the 
balances,  a  second  should  take  the  number  of  revolutions 
made  in  one  minute,  a  third  should  watch  the  ammeter  dur- 


Fig.   110. 


POWER  AND  EFFICIENCY  OF  A  MOTOR        293 


ing  the  minute  and  record  its  average  reading,  and  a  fourth 
should  do  the  same  for  the  voltmeter. 

(a)  After  the  connections  have  been  approved  by  the 
instructor,  start  the  motor.  Make  sure  that  it  is  running 
in  the  right  direction  and  that  the  voltmeter  and  ammeter 
are  connected  so  that  their  needles  read  in  the  right  di- 
rection. Adjust  the  tension  of  the  brake  by  raising  the 
supporting  arm,  so  that  the  ammeter  indicates  about  half 
as  much  current  as  the  normal  load  of  the  motor  requires. 
The  voltmeter,  ammeter,  and  spring  balances  should  then 
be  watched  for  one  minute,  while  the  speed  is  being  taken, 
and  all  readings  recorded.  A  second  set  of  readings 
should  be  taken  under  the  same  conditions.  If  there  is 
any  marked  variation  in  either  voltmeter  or  ammeter  read- 
ings during  either  minute,  the  results  for  that  minute 
should  be  discarded  and  another  reading  taken. 

(6)  Increase  the  tension  of  the  brake,  so  that  the  motor 
takes  the  full  number  of  amperes  for  which  it  is  designed. 
Make  two  sets  of  readings,  like  those  in  (a),  and  record. 


Diameter  of  pulley 


OBSERVATIONS 

Th ickn ess  of  strap         in. 


TRIAL 

BALANCE  READINGS 

SPEED 

PRESSURE 

CUBRENT 

High 

Low 

a-1 
a-2 
b-1 
b-2 

lb. 

lb. 

R.  P.  M. 

V. 

amp. 

lb. 
lb. 

lb. 
lb. 

R.  P.  M. 
R.  P.  M. 

V. 

v. 

amp. 
amp. 

lb. 

lb. 

R.  P.  M. 

v. 

amp. 

Make  a  diagram  of  the  electrical  connections  and  an 
outline  drawing  showing  the  brake  in  place  on  the  pulley; 
write  a  brief  description  of  the  method. 


294 


LABORATORY   EXERCISES 


Calculation  of  Horse  Power.  —  The  force  exerted  by  the 
pulley  on  the  brake  is  evidently  the  difference  between  the 
two  balance  readings,  as  when  the  pulley  is  turning  there 
is  more  pull  on  one  of  the  balances  and  less  on  the  other 
than  when  the  pulley  is  at  rest,  with  the  support  of  the 
brake  in  the  same  position.  As  a  large  portion  of  the 
pulley  is  always  in  contact  with  the  brake,  the  distance 
through  which  the  frictional  force  between  the  brake  and 
the  pulley  acts  in  a  minute  is  the  same  as  the  distance 
traveled  by  a  point  on  the  circumference  of  the  pulley  in 
a  minute.  In  calculating  this  circumference,  half  the 
thickness  of  the  belt  is  added  to  the  radius  of  the  pulley, 
and  this  measurement  is  reduced  to  feet.  So  the  work 
per  minute  equals  (difference  between  balance  readings) 
X  (diameter  of  pulley  +  thickness  of  belt)  x  TT  x  (revolu- 
tions per  minute).  Dividing  the  foot  pounds  per  minute 
by  33,000  gives  the  horse  power. 

Calculation  of  Efficiency.  —  The  horse  power  obtained 
multiplied  by  746  gives  the  power  output  in  watts.  The 
product  of  the  volts  and  amperes  gives  the  power  input  in 
watts.  The  former  divided  by  the  latter  is  the  efficiency. 

The  horse  power  and  the  efficiency  at  half  load  and  at 
full  load  should  be  calculated,  taking  the  average  of 
the  two  readings  in  (a)  for  one  calculation  ,and  the 
average  of  the  readings  in  (6)  for  the  other. 

CALCULATED  RESULTS 


TBIAL 

NET 
FORCE 

DISTANCE 

PER   MlN. 

FOOT  POUNDS 
PER  Mm. 

HORSE 
POWER 

WATTS 
OUTPUT 

WATTS 
INPUT 

EFFI- 
CIENCY 

a 

lb 

ft. 

ft.  lb. 

H.P. 

°/ 

b 

lb. 

ft. 

ft.  lb. 

H.P. 



% 

POWER  AND  EFFICIENCY  OF  A  MOTOR        295 

Discussion : 

Is  the  electrical  energy  consumed  by  a  given  motor 
independent  of  the  work  the  motor  is  doing  or  dependent 
upon  it?  Does  the  motor  always  work  at  full  horse 
power  ?  Is  it  better  economy  to  select  small  motors  for  a 
factory  and  run  them  at  full  load,  or  large  ones  and 
run  them  at  half  load  ?  Would  any  energy  be  required 
to  run  a  motor  with  no  external  load  ?  What  would  be 
the  efficiency  of  a  motor  at  no  load  ?  Is  the  change  in 
speed  of  your  motor  comparable  in  amount  to  the  change 
in  load  ? 

Conclusion : 

The  maximum  horse  power  obtained  from  the  motor 
tested  was H.P. 

The  efficiency  at  maximum  horse  power  was  %. 

The  efficiency  of  a  motor  is at  full  load  than  at 

partial  load. 


296 


LABORATORY    EXERCISES 


EXPERIMENT    87 

Relation  between  Fall  of  Potential  and  Resistance 

OBJECT.  To  determine  the  relation  between  the  fall  of  potential 
in  different  parts  of  a  circuit  and  the  resistance  of  those  parts  of  the 
circuit. 

APPARATUS.  H igh  resistance  wire,  #  22  Prima  Prima  (la  la) ,l 
mounted  on  a  meter  stick  ;  voltmeter,  low  reading  ;  ammeter,  low 
reading ;  sliding  contact ;  dry  or  storage  cells  to  give  about  6 
volts  ;  wire  for  connections. 

Introductory : 

When  a  power  house  is  delivering  current  to  some  dis- 
tant point,  it  is  found  that  the  voltage  is  higher  at  the 

power  house  than  at  the 
other  end  of  the  line. 
There  has  occurred  a 
drop  in  voltage,  which 
is  equal  to  the  pressure 
necessary  to  send  the 


Fig.   111. 


current  through  the  line. 

By  comparing  the  drop 
in  voltage  between  the  generator  and  different  points 
with  the  resistance  of  the  line  between  the  generator  and 
those  points,  the  relation  between  the  drop  in  any  part  of 
the  circuit  and  the  resistance  of  that  part  of  the  circuit 
may  be  determined. 

1  This  may  be  obtained  from  Hermann  Boker  and  Company,  101 
Duane  St.,  New  York.  German  silver  wire  may  be  used  instead,  but  its 
resistance  is  not  so  high  as  the  la  la,  and  the  latter  has  a  negligible  tem- 
perature coefficient. 


FALL  OF  POTENTIAL  AND  RESISTANCE         297 

Experimental : 

Connect  a  high  resistance  wire  1  meter  long  in  series 
with  an  ammeter  and  storage  cells.  To  the  zero  end  of 
the  wire  connect  the  proper  terminal  of  a  low-reading 
voltmeter.  Connect  the  other  terminal  of  the  voltmeter 
with  a  sliding  contact.  Examine  all  connections  to  see 
that  the  polarity  is  correct. 

Close  the  switch  and  place  the  sliding  contact  at  the 
end  of  the  wire  opposite  to  the  other  voltmeter  connection. 
Read  the  current,  the  length  of  the  wire,  and  the  potential 
difference  between  the  ends.  Move  the  sliding  contact 
10  cm.  toward  the  fixed  contact  and  read  as  before.  Re- 
peat, moving  10  cm.  at  a  time  until  the  fixed  and  movable 
contacts  touch. 

Record  all  readings  in  tabular  form  near  the  top  of  the 
left-hand  page. 

OBSERVATIONS 

128456789      10     11 

Length  of  resistance    100  90  80  70  60  50  40  30  20  10  0 

wire  in  cm. 
Potential  difference 

between  ends 

Current  strength  ., 

Make  a  diagram  showing  the  connections,  and,  referring 
to  the  diagram,  write  a  brief  description  of  the  method. 

From  the  laws  of  resistance,  we  may  assume  that  the 
resistance  of  different  lengths  of  the  wire  are  propor- 
tional to  the  lengths.  By  subtracting  each  reading  of 
length  from  100  cm.,  the  change  in  length  of  the  wire  is 
found.  By  subtracting  each  voltmeter  reading  from  the 
reading  for  the  whole  wire,  the  fall  of  potential  for  each 
change  of  length  is  found.  These  subtractions  should 


298  LABORATORY   EXERCISES 

be  made  in  order,  beginning  with  the  first  two  readings, 
and  the  results  recorded  in  the  table  at  the  top  of  the 
right-hand  page.  In  case  the  current  changes  during  the 
experiment,  calculate  the  resistance  of  each  10  cm.  length, 
and  record  the  changes  in  resistance  instead  of  the  changes 
in  length. 

CALCULATED  RESULTS 


Change  in  length  of  wire 
Fall  of  potential 


Discussion  : 

What  do  the  readings  of  the  ammeter  measure  ?  Those 
of  the  voltmeter?  How  could  the  actual  resistance  of  any 
part  of  the  wire  be  calculated?  If  the  current  remains 
constant,  to  what  do  you  attribute  the  differences  in  the 
fall  of  potential  in  different  lengths  of  the  wire  ? 

Conclusion  : 

What  is  the  relation  between  the  fall  of  potential  in 
different  parts  of  a  circuit  and  resistances  of  those  parts 
of  the  circuit  ? 


EXPERIMENT    88 

Resistance  by  the  Wheatstone  Bridge 

OBJECT.  To  measure  the  resistance  of  a  conductor  by  means  of 
the  Wheatstone  bridge. 

APPARATUS.  Wheatstone  bridge,  slide-wire  form;  galvanome- 
ter ;  contact  key  ;  plug  resistance  box  ;  Daniell  cell,  or  dry  cell  ; 
wire  for  connections  ;  three  coils  or  other  pieces  of  apparatus  for 
resistance  measurement  (resistance  about  6  to  15  ohms). 


RESISTANCE  BY  THE  WHEATSTONE  BRIDGE      299 


Introductory : 

The  Wheatstone  bridge  provides  a  rapid,  accurate 
method  of  measuring  a  wide  range  of  resistance  (1,000,000 
or  more  ohms  to  a  thousandth  of  an  ohm  with  some  forms 
of  bridge).  The  theory  of  the  bridge  is  based  on  Ohm's 
Law  of  the  fall  of  potential  in  a  circuit.  The  method 
of  its  use  depends  upon  comparing  the  ratio  between  a 
known  and  an  unknown  resist- 
ance, with  the  ratio  between 
two  known  resistances.  The 
four  resistances  are  connected 
as  shown  in  Fig.  112,  AB  con- 
taining the  unknown  resistance^ 
Rr  BC  a  resistance  box,  R±, 
and  AD  and  DO  resistances,  H2 
and  .R3,  whose  ratio  is  known. 

When    B   and  D   have    the 
potential    and 


Fig.  112. 


same  potential  ana  are  con- 
nected through  the  galvanometer,  no  current  will  flow. 
Hence  the  needle  is  not  deflected  and  the  bridge  is  said  to 
be  balanced.  The  ratio  ^i("nkp°wn)  .g  the  game  ag  ^ 


ratio 


—  2 


a   known    ratio.      In     the     slide-wire    bridge 


(Fig.  113),  AOB  is  a  uniform  wire,  so      =       = 

H      HU     length  (JB 

Thus,  when  the  bridge  is  balanced,  the  lengths  AB  and 
CB  are  measured,  the  resistance  R  is  known,  and  it  is  an 
easy  matter  to  calculate  the  unknown  resistance. 


Experimental : 

Arrange    the   apparatus   as   in    Fig.    113,   inserting   a 
single  contact  key  between  one  side  of  the  cell  and  the 


300  LABORATORY   EXERCISES 

bridge.  Notice  that  the  current  flows  in  a  divided  circuit 
through  the  bridge.  Trace  the  current  in  each  branch. 

Make  the  resistance  in  the  resistance  box  5  ohms  for  the 
first  test.  Close  the  key  in  the  battery  circuit,  and  then 
touch  the  wire  at  the  50  cm.  point  with  the  movable  gal- 
vanometer contact.  Observe  the  direction  and  the  amount 
of  deflection  of  the  galvanometer.  It  is  not  necessary  to 
record  these.  Increase  the  resistance  in  the  box  by  1  ohm, 
and  again  test.  Judge  by  the  direction  and  amount  of 

deflection   whether    the 
. R  .  resistance  in  the  box  is 

}  {  too  much  or  too  little. 

Change    the    resistance 
in  the  box  until  the  de- 
P.      113  flection    is    small,    and 

then  shift  the  movable 

contact  until  no  current  flows  through  the  galvanometer. 
Record  the  resistance  in  the  box  and  the  distance  of  the 
sliding  contact,  as  measured  from  each  end  of  the  metric 
scale,  in  a  tabular  form  near  the  top  of  the  left-hand  page. 
Also  specify  the  material  and  length  or  number  of  the  coil 
whose  resistance  is  being  measured. 

Make  a  similar  set  of  measurements  for  two  other  coils 
of  unknown  resistance. 

OBSERVATIONS 

DESCRIPTION  OF  RESISTANCE 

COIL  MEASURED  ra  Box  Jt  LENGTH  AC  LENGTH  CB 

ohms  cm.  cm. 

ohms  cm.  cm. 

ohms  cm.  __.  cm. 

Make  a  drawing  showing  the  arrangement  of  the  appa- 
ratus. Describe  the  method  of  balancing  the  bridge. 


RESISTANCE  BY  THE  WHEATSTONE  BRIDGE      301 

Let  X  represent  the  unknown  resistance.     When  the  re- 
sistance (.B)  has  been  found  for  which  no  current  flows 

v-     ^4(7 

through  the  galvanometer,  the  proportion  —  =  —  —  is  true. 

R      (JJ) 


Hence  X= 


Calculate  the  value  of  each  of  the  three  unknown  resist- 
ances. Record  in  tabular  form  at  the  top  of  the  right- 
hand  page. 

CALCULATED  RESULTS 

DESCKIPTION  OF  COIL  X  CALCULATED  RESISTANCE 

_______________  ohm  8 

_______________  ohms 

ohms 

Discussion  : 

X     A.O 

Explain  the  relation  —  =  —  —  by  the  principle  devel- 
R      CB 

oped  in  the  fall  of  potential  experiment  (Experiment  87, 
p.  296).  Under  what  conditions  only  will  no  current 
flow  through  the  galvanometer  circuit  ?  Show  that  this 
condition  can  be  proved  by  Ohm's  Law,  since  E  =  IR. 


302  LABORATORY   EXERCISES 

EXPERIMENT    89 

Induced  Currents 

OBJECT.  To  cause  induced  currents  to  flow  through  a  coil  of 
wire  and  to  determine  the  laws  of  such  currents. 

APPARATUS.  Coil  of  100  or  more  turns  of  fine  insulated  wire, 
so  wound  that  the  direction  of  winding  may  be  clearly  seen  ;  sen- 
sitive galvanometer  ;  strong  horseshoe  magnet,  such  as  is  used  in 
telephone  magnetos,  mounted  in  an  upright  position. 

Introductory : 

The  dynamo,  the  induction  coil,  and  the  transformer 
illustrate  the  production  of  electric  currents  through 
closed  circuits  of  wire  which  do  not  contain  any  voltaic 
cells.  In  each  of  these  cases,  an  electromotive  force  is 
produced  by  moving  coils  of  wire  in  such  a  way  that  they 
cut  magnetic  lines  of  force,  or  moving  the  lines  of  force  so 
that  they  cut  the  coil.  This  process  of  producing  an 
electromotive  force  is  called  electromagnetic  induction. 

Experimental : 

Connect  a  coil  of  fine  wire  with  a  sensitive  galvanom- 
eter. The  terminal  of  the  galvanometer  at  which  the 
current  enters  to  produce  a  deflection  in  a  given  direction 
must  be  known.  Support  a  horseshoe  magnet  in  an  up- 
right position  and  move  the  coil  rapidly  downward  over 
the  north  pole  of  the  magnet.  By  means  of  a  diagram  like 
Fig.  114,  record,  near  the  top  of  the  right-hand  page,  the 
direction  of  motion  of  the  coil,  the  direction  of  winding  of 
the  coil,  and  the  terminal  of  the  galvanometer  at  which 
the  current  enters.  This  terminal  should  be  marked  +. 
After  making  this  diagram,  indicate  by  arrowheads  the 


INDUCED  CURRENTS  303 

direction  which  the  current  takes  through  the  coil.  The 
deflection  of  the  galvanometer  is  to  be  recorded  beside  the 
diagram  as  "large"  or  "small."  Observe  whether  the 
induced  current  continues  after  the  motion  of  the  coil  has 
stopped. 

Allow  the  galvanometer  to  come  to  rest,  then  rapidly 
draw  off  the  coil,  observing  and  recording  as  before,  by 
means  of  another  diagram.     Repeat  the  test  with        ^_^^ 
the  south  pole.      Record  in  a  third  and  in  a        (  G  J 
fourth  diagram.     Repeat  any  one  of  the  tests,          |f_ 
moving  the  coil  more  slowly.     Record  in  a  fifth 
diagram.     Is  the  direction  of  deflection  the  same 
as  when  the  coil  was  moved  more  rapidly  ?     Is 
the  magnitude  of  deflection  the  same  ? 

Place  the  coil  over  one  pole  of  the  magnet, 
and  vary  the  magnetic  field  by  suddenly  pulling 

o*ff   the  armature.     This  causes  an  increase  in 

Fig.  114. 
the  lines  of  force  in  the  field  surrounding  the 

magnet.  Record  this  result  as  before  in  a  diagram.  Next 
suddenly  replace  the  armature,  thus  lessening  the  number 
of  lines  in  the  space  around  the  magnet,  and  record  this 
result. 

The  seven  diagrams  take  the  place  of  a  table  of  observa- 
tions. It  is  very  important  that  each  diagram  be  a  com- 
plete record  of  the  test  recorded  by  it ;  so  be  sure  that  the 
sign  of  the  pole,  the  direction  of  motion  of  the  coil,  the 
direction  of  current  in  the  coil,  and  the  relative  amount  of 
current  are  indicated. 

No  additional  drawing  is  necessary,  but  the  tests  made 
should  be  briefly  described. 

Discussion  • 

How  long  is  an  induced  electromotive  force  maintained  ? 
What  would  be  the  probable  effect  of  using  a  coil  of  a  less 


304  LABORATORY   EXERCISES 

number  of  turns  ?  When  the  coil  is  moving  toward  the 
pole  of  the  magnet,  does  the  pole  of  the  coil  attract  or 
repel  that  of  the  magnet  ? 

When  the  coil  is  moving  off  the  magnetic  pole,  is  there 
attraction  or  repulsion  between  its  pole  and  that  of  the 
magnet  ? 

Conclusion : 

How  may  an  electromotive  force  be  induced  ?  Upon 
what  does  the  direction  of  an  induced  electromotive  force 
depend?  Upon  what  does  the  amount  of  the  induced 
electromotive  force  depend  ? 


EXPERIMENT  9O 

• 

Study  of  a  Dynamo 

OBJECT.  To  observe  the  generation  of  current  in  a  simple 
dynamo  and  to  study  the  construction  of  a  direct  current  dynamo. 

APPARATUS.  Large  U-shaped  magnet,  mounted  with  its  poles 
vertical ;  coil  of  fine  wire  wound  on  a  wooden  or  an  iron  core,  to 
be  revolved  between  the  magnet  poles  ;  sensitive  galvanometer ; 
two-pole,  drum-wound  small  dynamo  (6-8  volts);  voltmeter; 
dry  or  storage  cell,  or  other  source  of  current  for  exciting  the 
field  of  the  dynamo. 

Introductory : 

Voltaic  cells  are  not  adapted  to  produce  high  pressures 
and  large  currents.  Hence  dynamos  are  employed  in 
commercial  work.  Their  action  depends  upon  the  fact 
that  when  a  conductor  cuts  across  magnetic  lines  of  force, 
a  difference  of  potential  is  produced  in  the  conductor. 
The  electromagnet  which  produced  the  lines  of  force  in  a 


STUDY  OF  A  DYNAMO 


305 


dynamo  is  called  the  field  magnet.  The  conductors  which 
cut  the  lines  are  wires  wound  about  a  soft  iron  core.  The 
wires  and  core  together  constitute  the  armature.  The 
current  generated  in  the  armature  is  led  out  into  the 
external  circuit  by  means  of  brushes,  which  make  a  sliding 
contact  with  bars  connected  to  the  ends  of  the  armature 
coils.  These  bars  may  be  so  placed  and  connected  that 
the  brushes  change  their  contact 
from  one  bar  to  the  next  at  just 
the  instant  when  the  difference  of 
potential  changes  direction.  The 
bars  then  constitute  the  commu- 
tator. We  shall  first  observe  the 
generation  of  voltage  in  a  simple 
dynamo  and  then  examine  a  ma- 
chine of  commercial  type  to  locate 
the  parts  just  described. 

Experimental : 

(a)  Connect  the  long,  flexible 
leads  of  the  armature  coil  fur- 
nished you  with  the  galvanom- 
eter (Fig.  115).  Hold  the  arm-  I 
ature  between  the  poles  of  the  coil 
in  a  vertical  position.  Turn  the 
coil  sharply  through  a  quarter  of  a  revolution  and  ob- 
serve the  behavior  of  the  galvanometer.  If  you  do  not 
know  from  the  direction  of  deflection  of  the  galvanometer 
the  direction  of  current  flow  in  the  two  connecting  wires, 
ask  the  instructor  to  show  you  how  to  determine  this. 
In  a  diagram  like  that  shown  in  Fig.  116,  A,  placed  near 
the  top  of  the  left-hand  page,  record  the  direction  of  rota- 
tion, the  direction  of  the  magnetic  field,  and  the  direction 
of  flow  of  current  in  the  wires  on  each  side  of  the  armature. 


Fig.   115. 


306 


LABORATORY   EXERCISES 


The  other  three  tests  to  be  made  are  to  be  recorded  in 
similar  diagrams,  placed  beside  this  one  (Fig.  116;  B,  C,  D). 
Turn  the  coil  through  the  next  quarter  turn,  observe 
the  direction  of  deflection  of  the  galvanometer,  and  record 
the  results  in  a  diagram  like  that  for  the  first  quarter  turn. 
Repeat  the  process  and  make  similar  records  for  the  third 
and  fourth  quarters  of  the  revolution.  The  current  in- 
duced in  this  simple  dynamo  is  an  alternating  current. 
In  how  many  directions  does  the  induced  current  flow  during 
one  complete  revolution  of  the  armature  f 


Fig.    116. 

(5)  This  part  of  the'  experiment  should  not  be  per- 
formed with  the  three-pole  armature  type  of  toy  motor 
or  generator. 

The  following  parts  of  the  dynamo  should  be  located, 
and  a  sketch  of  the  machine  made  showing  them :  field 
magnet,  armature,  brushes,  commutator.  Report  on  the 
following  points  of  construction  in  your  note-book : 

(1)  Where   and   how   the   connection   of   one   coil   to 
another  is  made. 

(2)  The  connections  made  to  each  commutator  segment. 
Connect  the  armature  terminals  to  a  voltmeter  or  to  the 

galvanometer  used  in  part  (a).  Supply  current  to  the 
field  from  a  dry  or  other  cell.  By  twisting  the  armature 
with  your  thumb  and  finger,  verify  the  statement  that 
voltage  is  produced  when  lines  of  force  are  cut.  Turn  the 


STUDY  OF  A  DYNAMO  307 

armature  in  the  opposite  direction  and  note  the  effect. 
Would  the  dynamo  generate  if  the  field  magnet  were  con- 
nected to  the  brushes,  instead  of  to  some  external  source  of 
current  ? 

The  description  should  include  the  results  of  any  obser- 
vations not  recorded  in  the  diagrams  called  for  above. 

Discussion : 

Answer  the  italicized  questions  occurring  in  the  experi- 
mental directions. 

Show  that  the  coils  are  so  connected  that  the  sum  of 
the  electromotive  forces  generated  in  them  shall  be  the 
electromotive  force  at  the  brushes. 

Conclusion : 

State  the  use  of  each  part  of  the  dynamo,  —  magnet, 
armature,  commutator,  brushes. 


APPENDIX 

I.    Important  Numbers  and  Equivalents 

TT  =  3.1416 
Tr2  =  9.8696 
Circumference  of  a  circle  =  trD 

•     Area  of  a  circle  =  Trr2  or  - — 
4 

1  centimeter  =  0.3937  in. 
1  inch  =  2.54  cm. 
1  mile  =  1.609  kilometers 
1  cubic  inch  =  16.387  cm.3 
1  pound  avoir.  =  453.6  g. 
1  ounce  avoir.  =  28.35  g. 
1  kilogram  =  2.2  Ib. 

1  liter  =  1.0567  qt.  (liquid) 
1  cm.3  water  at  4°  C.  =  1  g. 
1  ft.3  water  at  4°  C.  =  62.4  Ib. 
1  atmosphere  =  14.7  Ib. 
1  atmosphere  =  76  cm.  mercury 
1  atmosphere  =  30  in.  mercury 
1  atmosphere  =  33.57  ft.  water 
Energy  consumed  in  heating  1  Ib.  of  water  1°  F.  (1  B.  T.  U.) 

=  778  ft.  Ib.       . 
Energy  consumed  in  heating  1  g.  of  water  1°  C.  (1  calorie) 

=  3.09  ft.  Ib. 

1  British  Thermal  Unit  (B.  T.  U.)  =  252  calories 
1  horse  power  =  550  ft.  Ib.  per  second  =  33,000  ft.  Ib.  per  minute 

=  746  watts  =  f  kilowatt,  nearly 
1  kilowatt  =  1000  volt-amperes  =  *fffi  horse  power  =  £  horse 

power,  nearly 

Heat  in  calories  developed  by  resistance  =  0.24  x  amperes2  x 
ohms  x  seconds  =  0.24  watt-seconds 
309 


310 


APPENDIX 


000000000000         00 


6  6  o  o  o  o  o  o  d  o'  o'  o' 


g  o 

O     O 


1 1  1 1  I  3  § 


S  g 

'5  5 
0  £ 


2    c^ 


? 


.  . 


'  sf 


5  I  II 


I! 


o   O   O 


PROPERTIES  OF  MATERIALS 


311 


o    o    o 


I 

8? 


O     (-      » 

E  - 


-a 


312 


APPENDIX 


III.    Density  of  Water 

GEAMS  PER  CM.S 


TEMP.  »  C. 

DENSITY 

TEMP,  o  C. 

DENSITY 

TUMP.  •  C. 

DENSITY 

0° 

0.999868 

11° 

0.999632 

21° 

0.998019 

1 

0.999927 

12 

0.999525 

22 

0.997797 

2 

0.999968 

13 

0.999404 

23 

0.997565 

3 

0.999992 

14 

0.999271 

24 

0.997323 

4 

1.000000 

15 

0.999126 

25 

0.997071 

6 

0.999992 

16 

0.998970 

26 

0.996810 

6 

0.999986 

17 

0.998801 

27 

0.996539 

7 

0.999929 

18 

0.998622 

28 

0.996259 

8 

0.999876 

19 

0.998432 

29 

0.995971 

9 

0.999808 

20 

0.998230 

30 

0.995673 

10 

0.999727 

100 

0.95838 

IV.     Index  of  Refraction 


Water  .... 
Alcohol  .  .  . 
Carbon  bisulphide 


1.33 


1.64 


Crown  glass 1.51 

Flint  glass      .    .     .     .  1.54  to  1.71 
Diamond   .  .2.47 


V.     Electromotive  Force  of  Cells 


Simple  cell 1.0  volt 

Daniell  cell 1.1  volts 

Gravity  cell 1.1  volts 

Leclanche"  cell  .  .1.5  volts 


Dry  cell 

Bichromate  cell  .  . 
Storage  cell,  lead  .  . 
Storage  cell,  Edison  . 


1.5  volts 
2.0  volts 
2.0  volts 
1.2  volts 


NATURAL  SINES  AND  TANGENTS 


313 


VI.    Table  of  Natural  Sines  and  Tangents 


AN..I  r 

SINE 

TANGENT 

ANGLE 

SINK 

TANGENT 

ANGLE 

SINE 

TANGENT 

0 

0.000 

0-000 

31 

0.515 

0.601 

62 

0.883 

1.881 

1 

0.017 

0.017 

32 

0.530 

0.625 

63 

0.891 

1.963 

2 

0.035 

0.035 

33 

0.545 

0.649 

64 

0.899 

2.050 

8 

0.052 

0.052 

34 

0.559 

0.675 

65 

0.906 

2.145 

4 

0.070 

0.070 

35 

0.574 

0.700 

66 

0.914 

2.246 

5 

0.087 

0.087 

36 

0.588 

0.727 

67 

0.921 

2.356 

6 

0-105 

0.105 

37 

0.602 

0.754 

68 

0.927 

2.475 

7 

0.122 

0.123 

38 

0.616 

0.781 

69 

0.934 

2.605 

8 

0.139 

0-141 

39 

0.629 

0.810 

70 

0.940 

2.747 

9 

0.156 

0.158 

40 

0.643 

0.839 

71 

0.946 

2.904 

10 

0.174 

0.176 

41 

0.656 

0869 

72 

0.951 

3.078 

11 

0.191 

0.194 

42 

0.669 

0.900 

73 

0.956 

3.271 

12 

0.208 

0.213 

43 

0.682 

0.933 

74 

0.961 

3.487 

13 

0.225 

0.231 

44 

0.695 

0.966 

75 

0-966 

3.732 

14 

0.242 

0.249 

45 

0.707 

1.000 

76 

0.970 

•  4.011 

15 

0.259 

0.268 

46 

0.719 

1.036 

77 

0.974 

4.331 

16 

0.276 

0.287 

47 

0.731 

1.072 

78 

0.978 

4.705 

17 

0.292 

0.306 

48 

0.743 

1.111 

79 

0.982 

5.145 

18 

0.309 

0.325 

49 

0.755 

.150 

80 

0.985 

5.671 

19 

0.326 

0.344 

50 

0.766 

.192 

81 

0.988 

6.314 

20 

0.342 

0.364 

61 

0.777 

.235 

82 

0.990 

7.115 

21 

0.358 

0.384 

52 

0.788 

.280 

83 

0.993 

8-144 

22 

0.375 

0.404 

53 

0.799 

.327 

84 

0.995 

9.514 

23 

0.391 

0.424 

54 

0.809 

.376 

85 

0.996 

11.43 

24 

0.407 

0.445 

65 

0.819 

.428 

86 

0.998 

14.30 

25 

0.423 

0.466 

56 

0.829 

.483 

87 

0.999 

19.08 

26 

0.438 

0.488 

57 

0.839 

1.540 

88  • 

0.999 

28.64 

27 

0.454 

0.610 

58 

0.848 

1.600 

89 

1.000 

67.29 

28 

0.469 

0.532 

59 

0.867 

1.664 

90 

1.000 

Infinity 

29 

0.485 

O.fc-,4 

60 

0.866 

1.732 

30 

0.600 

0.577 

61 

0.876 

1.804 

314 


APPENDIX 


VII.    Size  and  Resistance  of  Annealed  Copper  Wire 


B.  &  S. 
GAUGE 

DIAMETER 
IN  MILS 

AREA  IN 

ClRClFJ.AE 

MILS 

OHMS  PER 

1000  FT. 

AT  20°  C. 

FEET  PER 
OHM  AT 
20°  C. 

FEET  PER  Lu., 
DOUBLE  COT- 
TON COVERED 

10 

101.89 

10,381 

0.997 

1,003 

30.9 

11 

90.74 

8,234 

1.257 

795.3 

38.9 

12 

80.81 

6,530 

1.586 

630.7 

48.8 

13 

71.96 

6,178 

1.999 

500.1 

61.5 

14 

64.08 

4,107 

2.621 

396.6 

77.4 

15 

57.07 

3,257 

3.179 

314.5 

97.2 

16 

60.82 

2,583 

4.009 

249.4 

121.9 

17 

45.26 

2,048 

6.055 

197.8 

163.1 

18 

40.30 

1,624 

6.374 

166.9 

191.5 

19 

35.89 

1,288 

8.038 

124.4 

246.9 

20 

31.96 

1,021 

10.14 

98.66 

297.9 

21 

28.46 

810.1 

12.78 

78.24 

374.6 

22 

25.36 

642.4 

16.12 

62.05 

471.7 

23' 

22.57 

509.4 

20.32 

49.21 

584.8 

24 

20.10 

404.0 

25.63 

39.02 

729.8 

25 

17.90 

320.4 

32.31 

31.29 

901.0 

26 

15.94 

254.1 

40.75 

24.54 

1123 

27 

14.19 

201.5 

51.38 

19.46 

1389 

28 

12.41 

159.8 

64.79 

15.43 

1695 

29 

11.26 

126.7 

81.70 

12.24 

2127 

30 

10.02 

100.5 

103.0 

9.707 

2564 

36 

5.00 

25.0 

414.2 

2.414 

6666 

It  will  be  noticed  that  the  area  of  $  13  wire  closely  approxi- 
mates one  half  that  of  $  10,  and  that  its  resistance  is  twice  as 
great.  Throughout  the  table,  an  increase  of  three  numbers  cor- 
responds to  doubling  the  resistance,  and  a  decrease  of  three 
numbers  to  halving  the  resistance. 


WIRE  CONSTANTS 


315 


VIII.    Specific  Resistance  and  Temperature  Coefficient 

(From  Timbie's  "Elements  of  Electricity") 


MATERIAL  (COMMERCIAL) 

SPECIFIC  RESISTANCE 
OHMS  PER  MIL-FOOT 

TEMPERATURE 
COEFFICIENT  = 
Increane  per  degree  C. 

« 

Jfesistanee  at  0"  C. 

Aluminum    .     .                         . 

17  4 

0  00435 

Copper  annealed 

10.4 

0.0042 

Copper,  hard  drawn  .... 
Iron   annealed 

10.65 
90 

0  005 

Iron,  E.  B.  B.  (Roebling)  .     . 
German  Silver       .... 

64 
114  to  275 

0.0046 
0.00025 

Manganin 

250  to  450 

0  00001 

la  la  (Boker),  soft     .... 
la  la  (Boker),  hard    .     .     .     . 
Advance  (Driver-Harris)^    .     . 

283 
300 
294 

0.000005 
0.00001 
0.00000 

SCIENCE 

First  Principles  of  Physics 

By  Professor  HENRY  S.  CARHART,  of  the  University  of  Michigan,  and 
H.  N.  CHUTE,  of  the  Ann  Arbor  High  School.  I2mo,  cloth,  422  pages. 
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It  has  been  felt  that  many  recent  text-books  in  physics  have 
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physics  in  attractiveness. 


SCIENCE 

A  Laboratory  Guide  to  accompany  Carhart  and  Chute's 
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67 


SCIENCE 

Physics  for  College  Students 

By  Professor  HENRY  S.  CARHART,  University  of  Michigan.     8vo, 
cloth,  631  pages.     Price,  #2.25. 

THIS  is  a  new  and  widely  successful  text-book  for  a  general 
course  in  Physics  in  colleges  and  universities.  In  writing  it 
the  author  has  kept  constantly  in  mind  those  students  who  are 
not  necessarily  scientific  in  their  taste  or  choice,  but  who  desire 
a  comprehensive  outline  of  the  leading  features  of  Physics. 
Mathematical  difficulties  have  been  successfully  reduced  to  such 
a  degree  that  they  may  be  readily  surmounted  by  the  average 
college  student. 

The  book  contains  a  full  treatment  of  Mechanics,  Sound,  Light, 
Heat,  and  Electricity  and  Magnetism. 


Physics  for  University  Students 

By  Professor  HENRY  S.  CARHART,  University  of  Michigan. 

Part  I:  Mechanics,  Sound,  and  Light.  Revised  edition  of  1906. 
With  154  Illustrations.  12010,  cloth,  346  pages.  Price,  $1.50. 

Part  II:  Heat,  Electricity,  and  Magnetism.  Revised  edition  of 
1904.  With  230  Illustrations.  I2mo,  cloth,  456  pages.  Price, 


THIS  is  a  revised  edition  of  the  work  which  has  for  ten  years 
been  so  favorably  known  to  professors  of  Physics.  The  two 
volumes  offer  a  more  extended  and  more  difficult  course  in  general 
Physics  than  the  Physics  for  College  Students  by  the  same  author. 

Only  such  topics  have  been  selected  as  appear  most  important 
to  a  general  survey  of  the  science.  Somewhat  more  attention 
than  is  customary  is  given  to  Simple  Harmonic  Motion,  because 
of  its  extensive  application  in  Alternating  Currents  and  its  service 
in  Mechanics,  Sound,  and  Light. 

Although  the  treatment  is  often  mathematical,  mathematics  is 
called  into  service  not  for  its  own  sake,  but  wholly  for  the  pur- 
pose of  establishing  the  relations  of  physical  quantities. 


SCIENCE 

Exercises  in  Physical  Measurement 

By  Professors  L.  W.  AUSTIN,  University  of  Wisconsin,  and  C.  B. 
THWING,  Syracuse  University.  i2mo,  cloth,  208  pages.  Price,  $1.50. 

THIS  book  is  a  laboratory  manual  for  the  first  year  of  the  col- 
lege or  university. 

Part  I  has  those  exercises  which  are  in  the  practicum  of  the 
best  German  universities.  They  are  exclusively  quantitative,  and 
the  apparatus  required  is  inexpensive. 

Part  II  contains  suggestions  regarding  computations  and  im- 
portant physical  manipulations. 

Part  III  contains  in  tabular  form  the  necessary  data. 

Electrical  Measurements 

By  Professor  HENRY  S.  CARHART  and  Professor  G.  W.  PATTERSON, 
University  of  Michigan.  I2mo,  cloth,  344  pages.  Price,  $2.00. 

QUANTITATIVE  experiments  only  have  been  introduced, 
and  these  have  been  selected  with  the  object  of  illustrating 
general  methods  rather  than  applications  to  specific  departments 
of  technical  work. 

Principles  of  Physics 

By  FRANK  M.  GILLEY,  of  the  Chelsea  High  School.  I2mo,  cloth, 
560  pages.  Price,  $1.30. 

THE  Principles  of  Physics  is  intended  for  use  in  the  laboratory 
or  classroom,  or  both.     The   author  has  made  many  im- 
provements  on   the   apparatus   hitherto  in  use,  in  many  cases 
materially  shortening  the  time  in  which  the  experiment  may  be 
performed,  or  facilitating  its  performance  by  large  classes. 

Elements  of  Physics 

By  Professor  HENRY  S.  CARHART,  of  the  University  of  Michigan,  and 
H.  N.  CHUTE,  of  the  Ann  Arbor  High  School.  I2mo,  cloth,  408  pages. 
Price,  $1.20. 

69 


BOOKKEEPING 


Practical  Bookkeeping 

By  CARLOS  B.  ELLIS,   Principal  of   the  Commercial    High  School 
of  Springfield,  Massachusetts.    8vo,  cloth,  256  pages.    Price,  $1.35. 

*^pHIS  manual  offers  a  complete  and  adequate  course  in  book- 
J-    keeping  that  will  enable  a  pupil  to  master  the  principles  of 
the  subject  and  give  him  sufficient  practice  in  their  application  to 
meet  the  ordinary  demands  of  business. 

The  method  of  the  book  is  to  appeal  to  the  pupil's  intelligence, 
not  to  his  memory ;  to  teach  by  explanation,  not  by  abstract 
rules. 

The  following  are  some  of  its  distinctive  features  : 

1.  The  subject  is  developed  logically  by  first  studying7  the 
ledger.     Since  each  entry  in  a  journal  or  other  book  of  original 
entry  is  to  be  posted  to  some  account  in  the  ledger,  it  is  mani- 
fest that  a  pupil  cannot  make  these  entries  intelligently  until  he 
understands  the  accounts  involved.     When  he  understands  the 
use  and  purpose  of  each  of  the  principal  accounts,  he  is  ready  to 
study  the  books  of  original  entry. 

2.  No  exercises  are  introduced  simply  with  the  purpose  of 
providing  work  and  prolonging  the  time  devoted  to  the  subject, 
but  there  is  enough  work  to  fit  the  pupil  to  meet  the  usual  re- 
quirements of  the  business  office. 

3.  The  exercises  for  supplementary  drill  cover  a  great  variety 
of  difficult  entries,  and  will  be  found  very  helpful. 

4.  Self-reliance  is  stimulated  by  special  instructions  for  the 
pupil,  given  at  points  where  they  will  be  needed.     The  author 
has  made  a  careful  study  of  the  pupils'  most  frequent  errors  and 
has  set  up  "  danger  signals  "  to  show  how  they  may  be  avoided. 

5.  No  attempt  is  made  to  teach  any  particular  business,  but  the 
several  sets  of  transactions  are  designed  solely  to  teach  the  prin- 
ciples of  bookkeeping. 

6.  The  book  is  unique  in  its  treatment  of  the  following  topics, 
each  of  which  has  been  prepared  by  an  expert :   The  Voucher 
Method ;  Loose-Leaf  Accounting ;  Card  Index  Systems ;  and  Fil- 
ing Systems. 

88 


BOOKKEEPING 


Blank  Books,  Forms,  and  Vouchers  to  accompany 
Ellis's  Bookkeeping 

BLANK  BOOKS. —  Parti.    Set  of  four.    Price,  50  cents. 
BLANK  BOOKS.  —  Part  II.    Set  of  five.     Price,  75  cents. 
BUSINESS  FORMS.    Price,  60  cents. 
INCOMING  VOUCHERS.    Price,  50  cents. 

Blank  Books  for  Part  I  Blank  Books  for  Part  II 

Journal  —  20  pages.  Journal  —  32  pages. 

Cash    Book    and    Sales    Book —  Cash  Book  —  24  pages. 

20  pages.  Sales  Book,  Purchase  Book,  and 

Ledger  —  44  pages.  Bill  Book  —  28  pages. 

Trial  Balances  and  Statements —  Ledger  —  76  pages. 

48  pages.  Trial    Balances  and  Statements  — 
44  pages. 

THESE  blank  books  are  very  neat  and  attractive  in  appear- 
ance, and  the  quality  of  the  paper  is  superior.     Those  for 
Part  II  have  special  rulings  and  printed  headings. 

Business  Forms 

This  package  contains  everything  the  pupil  will  need  for  Exer- 
cises XII  to  XIV.  It  includes  a  check  book,  a  substantial  office 
file,  and  a  generous  supply  of  stationery  and  forms.  Care  is  taken 
to  make  them  seem  like  actual  business  papers. 

Incoming  Vouchers 

These  vouchers  have  been  prepared  for  use  with  Exercises  XII 
to  XIV,  and  they  are  numbered  to  correspond  with  the  transac- 
tions in  the  text-book.  These  vouchers  are  characterized  by 
simplicity  and  neatness  of  design  and  a  businesslike  appearance. 

In  preparing  the  apparatus  Mr.  Ellis  has  improved  upon  the 
best  characteristics  of  all  similar  forms. 

NOTE.  —  On  the  outfit  to  accompany  Ellis's  Bookkeeping  transporta- 
tion is  at  the  expense  of  the  purchaser. 


University  of  California 

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Return  this  material  to  the  library  from  which  it  was  borrowed. 


OCT  1  6  2008 


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